// https://contest.ucup.ac/contest/1865/problem/9809
pub mod solution {
//{"name":"L. The Grand Contest","group":"Universal Cup - The 3rd Universal Cup. Stage 19: Shenyang","url":"https://contest.ucup.ac/contest/1865/problem/9809","interactive":false,"timeLimit":1000,"tests":[{"input":"2\n6 20\n1 1 60 0\n2 2 60 0\n2 2 120 1\n1 2 180 1\n1 2 180 0\n2 2 300 1\n2 20\n1 1 300 1\n2 2 300 1\n","output":"120 160\n-1\n"}],"testType":"single","input":{"type":"stdin","fileName":null,"pattern":null},"output":{"type":"stdout","fileName":null,"pattern":null},"languages":{"java":{"taskClass":"LTheGrandContest"}}}

use crate::algo_lib::collections::default_map::default_hash_map::DefaultHashMap;
use crate::algo_lib::collections::fx_hash_map::FxHashSet;
use crate::algo_lib::collections::iter_ext::iter_copied::ItersCopied;
use crate::algo_lib::collections::min_max::MinimMaxim;
use crate::algo_lib::collections::segment_tree::SegmentTree;
use crate::algo_lib::collections::segment_tree::SegmentTreeNode;
use crate::algo_lib::collections::slice_ext::backward::Back;
use crate::algo_lib::collections::slice_ext::bounds::Bounds;
use crate::algo_lib::collections::slice_ext::compress::compress;
use crate::algo_lib::collections::slice_ext::compress::Compressed;
use crate::algo_lib::collections::slice_ext::indices::Indices;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::direction::Direction;
use crate::algo_lib::misc::test_type::TaskType;

use crate::algo_lib::misc::test_type::TestType;
use crate::algo_lib::numbers::num_utils::PartialSums;
use crate::algo_lib::numbers::num_utils::UpperDiv;

type PreCalc = ();

fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let n = input.read_size();
    let p = input.read_long();
    let submissions = input.read_vec::<(usize, usize, i64, usize)>(n);

    let mut score = [0; 2];
    let mut penalty = [0; 2];
    let mut solve_at = vec![Vec::new(); 2];
    let mut solved = vec![FxHashSet::default(); 2];
    let mut submits = vec![DefaultHashMap::<_, i64>::new(); 2];
    for (team, problem, time, verdict) in submissions.copy_iter() {
        let team = team - 1;
        if solved[team].contains(&problem) {
            continue;
        }
        if verdict == 1 {
            penalty[team] += time + submits[team][problem] * p;
            score[team] += 1;
            solved[team].insert(problem);
            solve_at[team].push(time);
        } else {
            submits[team][problem] += 1;
        }
    }
    if score[0] != score[1] || score[0] == 0 {
        out.print_line(-1);
        return;
    }
    let need = if penalty[0] <= penalty[1] {
        penalty[1] - penalty[0] + 1
    } else {
        solve_at.swap(0, 1);
        penalty[0] - penalty[1]
    };

    let s0 = solve_at[0].clone();
    let s1 = solve_at[1].clone();
    let Compressed {
        order: poi,
        arrs: [s0, s1],
    } = compress([&s0, &s1]);
    let mut len = vec![0; poi.len()];
    for i in poi.indices() {
        len[i] = poi[i] - if i > 0 { poi[i - 1] } else { 0 };
    }
    let mut delta = vec![0; poi.len()];
    for (mult, s) in [(-1, s0), (1, s1)] {
        let mut cur = 0;
        let mut x = score[0];
        for i in s {
            for i in cur..=i {
                delta[i] += mult * x;
            }
            x -= 1;
            cur = i + 1;
        }
    }

    let mut ans = None;
    let total = poi[Back(0)];
    for reversed in [false, true] {
        #[derive(Default, Clone)]
        struct Node {
            sum: i64,
            max: i64,
        }
        impl SegmentTreeNode for Node {
            fn new(_left: usize, _right: usize) -> Self {
                Self::default()
            }

            fn join(&mut self, left_val: &Self, right_val: &Self) {
                self.sum = left_val.sum + right_val.sum;
                self.max = left_val.max.max(left_val.sum + right_val.max);
            }

            fn accumulate(&mut self, _value: &Self) {}

            fn reset_delta(&mut self) {}
        }
        let mut st = SegmentTree::<Node>::new(poi.len());
        let s = len.partial_sums();
        for i in poi.indices().rev() {
            st.point_update(
                i,
                Node {
                    sum: delta[i] * len[i],
                    max: (delta[i] * len[i]).max(0),
                },
            );
            if st.query(..).max < need {
                continue;
            }
            let mut need_rem = need;
            let pos = st.binary_search(
                |left, _right| {
                    if left.max >= need_rem {
                        Direction::Left
                    } else {
                        need_rem -= left.sum;
                        Direction::Right
                    }
                },
                |_, pos| pos,
            );
            assert!(delta[pos] > 0);
            let end = s[pos] + need_rem.upper_div(delta[pos]);
            let cur_len = end - s[i];
            let (start, end) = if reversed {
                (total - end, total - s[i])
            } else {
                (s[i], end)
            };
            ans.minim((cur_len, start, end));
        }
        len.reverse();
        delta.reverse();
    }
    if ans.is_none() {
        out.print_line(-1);
        return;
    }
    let (_, mut l, mut r) = ans.unwrap();
    let p0 = poi.lower_bound(&l);
    let p1 = poi.lower_bound(&r);
    if p0 != p1 {
        let p0_prev = if p0 > 0 { poi[p0 - 1] } else { 0 };
        let p1_prev = if p1 > 0 { poi[p1 - 1] } else { 0 };
        let mut total = 0;
        for i in p0 + 1..p1 {
            total += delta[i] * len[i];
        }
        total += (poi[p0] - l) * delta[p0] + (r - p1_prev) * delta[p1];
        let max = (poi[p0] - p0_prev).min(poi[p1] - p1_prev);
        let cur = delta[p1] - delta[p0];
        assert!(cur > 0);
        let shift = ((total - need) / cur).min(max);
        l -= shift;
        r -= shift;
    }
    out.print_line((l, r));
}

pub static TEST_TYPE: TestType = TestType::MultiNumber;
pub static TASK_TYPE: TaskType = TaskType::Classic;

pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    let mut pre_calc = ();

    match TEST_TYPE {
        TestType::Single => solve(&mut input, &mut output, 1, &mut pre_calc),
        TestType::MultiNumber => {
            let t = input.read();
            for i in 1..=t {
                solve(&mut input, &mut output, i, &mut pre_calc);
            }
        }
        TestType::MultiEof => {
            let mut i = 1;
            while input.peek().is_some() {
                solve(&mut input, &mut output, i, &mut pre_calc);
                i += 1;
            }
        }
    }
    output.flush();
    match TASK_TYPE {
        TaskType::Classic => input.is_empty(),
        TaskType::Interactive => true,
    }
}

}
pub mod algo_lib {
#![allow(clippy::too_many_arguments)]
#![allow(clippy::type_complexity)]
#![allow(clippy::missing_safety_doc)]
#![allow(clippy::legacy_numeric_constants)]

pub mod collections {
pub mod bounds {
use std::ops::RangeBounds;

pub fn clamp(range: impl RangeBounds<usize>, n: usize) -> (usize, usize) {
    let start = match range.start_bound() {
        std::ops::Bound::Included(&x) => x,
        std::ops::Bound::Excluded(&x) => x + 1,
        std::ops::Bound::Unbounded => 0,
    };
    let end = match range.end_bound() {
        std::ops::Bound::Included(&x) => x + 1,
        std::ops::Bound::Excluded(&x) => x,
        std::ops::Bound::Unbounded => n,
    };
    (start, end.min(n))
}
}
pub mod default_map {
pub mod default_hash_map {
use crate::algo_lib::collections::fx_hash_map::FxHashMap;
use std::hash::Hash;
use std::iter::FromIterator;
use std::ops::Deref;
use std::ops::DerefMut;
use std::ops::Index;
use std::ops::IndexMut;

#[derive(Default, Clone, Eq, PartialEq, Debug)]
pub struct DefaultHashMap<K: Hash + Eq, V>(FxHashMap<K, V>, V);

impl<K: Hash + Eq, V> Deref for DefaultHashMap<K, V> {
    type Target = FxHashMap<K, V>;

    fn deref(&self) -> &Self::Target {
        &self.0
    }
}

impl<K: Hash + Eq, V> DerefMut for DefaultHashMap<K, V> {
    fn deref_mut(&mut self) -> &mut Self::Target {
        &mut self.0
    }
}

impl<K: Hash + Eq, V: Default> DefaultHashMap<K, V> {
    pub fn new() -> Self {
        Self(FxHashMap::default(), V::default())
    }

    pub fn get(&self, key: &K) -> &V {
        self.0.get(key).unwrap_or(&self.1)
    }

    pub fn get_mut(&mut self, key: K) -> &mut V {
        self.0.entry(key).or_insert_with(|| V::default())
    }

    pub fn into_values(self) -> std::collections::hash_map::IntoValues<K, V> {
        self.0.into_values()
    }
}

impl<K: Hash + Eq, V: Default> Index<K> for DefaultHashMap<K, V> {
    type Output = V;

    fn index(&self, index: K) -> &Self::Output {
        self.get(&index)
    }
}

impl<K: Hash + Eq, V: Default> IndexMut<K> for DefaultHashMap<K, V> {
    fn index_mut(&mut self, index: K) -> &mut Self::Output {
        self.get_mut(index)
    }
}

impl<K: Hash + Eq, V> IntoIterator for DefaultHashMap<K, V> {
    type Item = (K, V);
    type IntoIter = std::collections::hash_map::IntoIter<K, V>;

    fn into_iter(self) -> Self::IntoIter {
        self.0.into_iter()
    }
}

impl<K: Hash + Eq, V: Default> FromIterator<(K, V)> for DefaultHashMap<K, V> {
    fn from_iter<T: IntoIterator<Item = (K, V)>>(iter: T) -> Self {
        Self(iter.into_iter().collect(), V::default())
    }
}
}
}
pub mod fx_hash_map {
// Copyright 2015 The Rust Project Developers. See the COPYRIGHT at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

use std::cell::Cell;
use std::convert::TryInto;
use std::time::SystemTime;
use std::collections::HashMap;
use std::collections::HashSet;
use std::hash::BuildHasherDefault;
use std::hash::Hasher;
use std::mem::size_of;
use std::ops::BitXor;

pub type FxHashMap<K, V> = HashMap<K, V, BuildHasherDefault<FxHasher>>;

pub type FxHashSet<V> = HashSet<V, BuildHasherDefault<FxHasher>>;

#[derive(Default)]
pub struct FxHasher {
    hash: usize,
}

thread_local! {
    static K: Cell<usize> = Cell::new(
        ((SystemTime::UNIX_EPOCH.elapsed().unwrap().as_nanos().wrapping_mul(2) + 1) & 0xFFFFFFFFFFFFFFFF) as usize
    );
}

impl FxHasher {
    #[inline]
    fn add_to_hash(&mut self, i: usize) {
        self.hash = self
            .hash
            .rotate_left(5)
            .bitxor(i)
            .wrapping_mul(K.with(|k| k.get()));
    }
}

impl Hasher for FxHasher {
    #[inline]
    fn write(&mut self, mut bytes: &[u8]) {
        let read_usize = |bytes: &[u8]| u64::from_ne_bytes(bytes[..8].try_into().unwrap());

        let mut hash = FxHasher { hash: self.hash };
        while bytes.len() >= size_of::<usize>() {
            hash.add_to_hash(read_usize(bytes) as usize);
            bytes = &bytes[size_of::<usize>()..];
        }
        if (size_of::<usize>() > 4) && (bytes.len() >= 4) {
            hash.add_to_hash(u32::from_ne_bytes(bytes[..4].try_into().unwrap()) as usize);
            bytes = &bytes[4..];
        }
        if (size_of::<usize>() > 2) && bytes.len() >= 2 {
            hash.add_to_hash(u16::from_ne_bytes(bytes[..2].try_into().unwrap()) as usize);
            bytes = &bytes[2..];
        }
        if (size_of::<usize>() > 1) && !bytes.is_empty() {
            hash.add_to_hash(bytes[0] as usize);
        }
        self.hash = hash.hash;
    }

    #[inline]
    fn write_u8(&mut self, i: u8) {
        self.add_to_hash(i as usize);
    }

    #[inline]
    fn write_u16(&mut self, i: u16) {
        self.add_to_hash(i as usize);
    }

    #[inline]
    fn write_u32(&mut self, i: u32) {
        self.add_to_hash(i as usize);
    }

    #[inline]
    fn write_u64(&mut self, i: u64) {
        self.add_to_hash(i as usize);
    }

    #[inline]
    fn write_usize(&mut self, i: usize) {
        self.add_to_hash(i);
    }

    #[inline]
    fn finish(&self) -> u64 {
        self.hash as u64
    }
}
}
pub mod iter_ext {
pub mod iter_copied {
use std::iter::Chain;
use std::iter::Copied;
use std::iter::Enumerate;
use std::iter::Filter;
use std::iter::Map;
use std::iter::Rev;
use std::iter::Skip;
use std::iter::StepBy;
use std::iter::Sum;
use std::iter::Take;
use std::iter::Zip;

pub trait ItersCopied<'a, T: 'a + Copy>: Sized + 'a
where
    &'a Self: IntoIterator<Item = &'a T>,
{
    fn copy_iter(&'a self) -> Copied<<&'a Self as IntoIterator>::IntoIter> {
        self.into_iter().copied()
    }
    fn copy_enumerate(&'a self) -> Enumerate<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().enumerate()
    }
    fn copy_rev(&'a self) -> Rev<Copied<<&'a Self as IntoIterator>::IntoIter>>
    where
        Copied<<&'a Self as IntoIterator>::IntoIter>: DoubleEndedIterator,
    {
        self.copy_iter().rev()
    }
    fn copy_skip(&'a self, n: usize) -> Skip<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().skip(n)
    }
    fn copy_take(&'a self, n: usize) -> Take<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().take(n)
    }
    fn copy_chain<V>(
        &'a self,
        chained: &'a V,
    ) -> Chain<
        Copied<<&'a Self as IntoIterator>::IntoIter>,
        Copied<<&'a V as IntoIterator>::IntoIter>,
    >
    where
        &'a V: IntoIterator<Item = &'a T>,
    {
        self.copy_iter().chain(chained.into_iter().copied())
    }
    fn copy_zip<V>(
        &'a self,
        other: &'a V,
    ) -> Zip<Copied<<&'a Self as IntoIterator>::IntoIter>, Copied<<&'a V as IntoIterator>::IntoIter>>
    where
        &'a V: IntoIterator<Item = &'a T>,
    {
        self.copy_iter().zip(other.into_iter().copied())
    }
    fn copy_max(&'a self) -> T
    where
        T: Ord,
    {
        self.copy_iter().max().unwrap()
    }
    fn copy_max_by_key<B, F>(&'a self, f: F) -> T
    where
        F: FnMut(&T) -> B,
        B: Ord,
    {
        self.copy_iter().max_by_key(f).unwrap()
    }
    fn copy_min(&'a self) -> T
    where
        T: Ord,
    {
        self.copy_iter().min().unwrap()
    }
    fn copy_min_by_key<B, F>(&'a self, f: F) -> T
    where
        F: FnMut(&T) -> B,
        B: Ord,
    {
        self.copy_iter().min_by_key(f).unwrap()
    }
    fn copy_sum(&'a self) -> T
    where
        T: Sum<T>,
    {
        self.copy_iter().sum()
    }
    fn copy_map<F, U>(&'a self, f: F) -> Map<Copied<<&'a Self as IntoIterator>::IntoIter>, F>
    where
        F: FnMut(T) -> U,
    {
        self.copy_iter().map(f)
    }
    fn copy_all(&'a self, f: impl FnMut(T) -> bool) -> bool {
        self.copy_iter().all(f)
    }
    fn copy_any(&'a self, f: impl FnMut(T) -> bool) -> bool {
        self.copy_iter().any(f)
    }
    fn copy_step_by(&'a self, step: usize) -> StepBy<Copied<<&'a Self as IntoIterator>::IntoIter>> {
        self.copy_iter().step_by(step)
    }
    fn copy_filter<F: FnMut(&T) -> bool>(
        &'a self,
        f: F,
    ) -> Filter<Copied<<&'a Self as IntoIterator>::IntoIter>, F> {
        self.copy_iter().filter(f)
    }
    fn copy_fold<Acc, F>(&'a self, init: Acc, f: F) -> Acc
    where
        F: FnMut(Acc, T) -> Acc,
    {
        self.copy_iter().fold(init, f)
    }
    fn copy_reduce<F>(&'a self, f: F) -> Option<T>
    where
        F: FnMut(T, T) -> T,
    {
        self.copy_iter().reduce(f)
    }
    fn copy_position<P>(&'a self, predicate: P) -> Option<usize>
    where
        P: FnMut(T) -> bool,
    {
        self.copy_iter().position(predicate)
    }
}

impl<'a, U: 'a, T: 'a + Copy> ItersCopied<'a, T> for U where &'a U: IntoIterator<Item = &'a T> {}
}
}
pub mod min_max {
pub trait MinimMaxim<Rhs = Self>: PartialOrd + Sized {
    fn minim(&mut self, other: Rhs) -> bool;

    fn maxim(&mut self, other: Rhs) -> bool;
}

impl<T: PartialOrd> MinimMaxim for T {
    fn minim(&mut self, other: Self) -> bool {
        if other < *self {
            *self = other;
            true
        } else {
            false
        }
    }

    fn maxim(&mut self, other: Self) -> bool {
        if other > *self {
            *self = other;
            true
        } else {
            false
        }
    }
}

impl<T: PartialOrd> MinimMaxim<T> for Option<T> {
    fn minim(&mut self, other: T) -> bool {
        match self {
            None => {
                *self = Some(other);
                true
            }
            Some(v) => v.minim(other),
        }
    }

    fn maxim(&mut self, other: T) -> bool {
        match self {
            None => {
                *self = Some(other);
                true
            }
            Some(v) => v.maxim(other),
        }
    }
}
}
pub mod segment_tree {
use crate::algo_lib::collections::bounds::clamp;
use crate::algo_lib::misc::direction::Direction;
use crate::algo_lib::numbers::num_traits::algebra::One;
use crate::algo_lib::numbers::num_traits::algebra::Zero;
use crate::when;
use std::marker::PhantomData;
use std::ops::Add;
use std::ops::MulAssign;
use std::ops::RangeBounds;

pub trait SegmentTreeNode {
    fn new(left: usize, right: usize) -> Self;
    fn join(&mut self, left_val: &Self, right_val: &Self);
    fn accumulate(&mut self, value: &Self);
    fn reset_delta(&mut self);
}

pub trait Pushable<T>: SegmentTreeNode {
    fn push(&mut self, delta: T);
}

impl<T: SegmentTreeNode> Pushable<&T> for T {
    fn push(&mut self, delta: &T) {
        self.accumulate(delta);
    }
}

impl<T: SegmentTreeNode> Pushable<T> for T {
    fn push(&mut self, delta: T) {
        *self = delta;
    }
}

pub trait QueryResult<Result, Args>: SegmentTreeNode {
    fn empty_result(args: &Args) -> Result;
    fn result(&self, args: &Args) -> Result;
    fn join_results(
        left_res: Result,
        right_res: Result,
        args: &Args,
        left: usize,
        mid: usize,
        right: usize,
    ) -> Result;
}

impl<T: SegmentTreeNode + Clone> QueryResult<T, ()> for T {
    fn empty_result(_: &()) -> T {
        Self::new(0, 0)
    }

    fn result(&self, _: &()) -> T {
        self.clone()
    }

    fn join_results(left_res: T, right_res: T, _: &(), left: usize, mid: usize, right: usize) -> T {
        when! {
            left == mid => right_res,
            right == mid => left_res,
            else => {
                let mut res = Self::new(left, right);
                res.join(&left_res, &right_res);
                res
            },
        }
    }
}

impl<
        Key: Add<Output = Key> + MulAssign<Delta> + Zero + Copy,
        Delta: MulAssign<Delta> + One + Copy,
    > SegmentTreeNode for (Key, Delta)
{
    fn new(_left: usize, _right: usize) -> Self {
        (Key::zero(), Delta::one())
    }

    fn join(&mut self, left_val: &Self, right_val: &Self) {
        self.0 = left_val.0 + right_val.0;
    }

    fn accumulate(&mut self, value: &Self) {
        self.0 *= value.1;
        self.1 *= value.1;
    }

    fn reset_delta(&mut self) {
        self.1 = Delta::one();
    }
}

#[derive(Clone)]
pub struct SegmentTree<Node> {
    n: usize,
    nodes: Vec<Node>,
}

impl<Node: SegmentTreeNode> SegmentTree<Node> {
    pub fn new(n: usize) -> Self {
        Self::from_generator(n, |left| Node::new(left, left + 1))
    }

    pub fn from_array(arr: Vec<Node>) -> Self {
        let n = arr.len();
        let mut iter = arr.into_iter();
        Self::from_generator(n, |_| iter.next().unwrap())
    }

    pub fn from_generator<F>(n: usize, gen: F) -> Self
    where
        F: FnMut(usize) -> Node,
    {
        if n == 0 {
            return Self {
                n,
                nodes: vec![Node::new(0, 0)],
            };
        }
        let mut res = Self {
            n,
            nodes: Vec::with_capacity(2 * n - 1),
        };
        res.init(gen);
        res
    }

    fn init<F>(&mut self, mut f: F)
    where
        F: FnMut(usize) -> Node,
    {
        self.init_impl(2 * self.n - 2, 0, self.n, &mut f);
    }

    fn init_impl<F>(&mut self, root: usize, left: usize, right: usize, f: &mut F)
    where
        F: FnMut(usize) -> Node,
    {
        if left + 1 == right {
            self.nodes.push(f(left));
        } else {
            let mid = left + ((right - left) >> 1);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            self.init_impl(left_child, left, mid, f);
            self.init_impl(right_child, mid, right, f);
            let mut node = Node::new(left, right);
            node.join(&self.nodes[left_child], &self.nodes[right_child]);
            self.nodes.push(node);
        }
    }

    pub fn point_query(&mut self, at: usize) -> &Node {
        assert!(at < self.n);
        self.do_point_query(self.nodes.len() - 1, 0, self.n, at)
    }

    fn do_point_query(&mut self, root: usize, left: usize, right: usize, at: usize) -> &Node {
        if left + 1 == right {
            &self.nodes[root]
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            if at < mid {
                self.do_point_query(left_child, left, mid, at)
            } else {
                self.do_point_query(right_child, mid, right, at)
            }
        }
    }

    pub fn point_update<T>(&mut self, at: usize, val: T)
    where
        Node: Pushable<T>,
    {
        assert!(at < self.n);
        self.do_point_update(self.nodes.len() - 1, 0, self.n, at, val);
    }

    fn do_point_update<T>(&mut self, root: usize, left: usize, right: usize, at: usize, val: T)
    where
        Node: Pushable<T>,
    {
        if left + 1 == right {
            self.nodes[root].push(val);
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            if at < mid {
                self.do_point_update(left_child, left, mid, at, val);
            } else {
                self.do_point_update(right_child, mid, right, at, val);
            }
            self.join(root, mid, right);
        }
    }

    pub fn point_through_update<'a, T>(&mut self, at: usize, val: &'a T)
    where
        Node: Pushable<&'a T>,
    {
        assert!(at < self.n);
        self.do_point_through_update(self.nodes.len() - 1, 0, self.n, at, val);
    }

    fn do_point_through_update<'a, T>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        at: usize,
        val: &'a T,
    ) where
        Node: Pushable<&'a T>,
    {
        self.nodes[root].push(val);
        if left + 1 != right {
            let mid = (left + right) >> 1;
            self.push_down(root, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            if at < mid {
                self.do_point_through_update(left_child, left, mid, at, val);
            } else {
                self.do_point_through_update(right_child, mid, right, at, val);
            }
        }
    }

    pub fn point_operation<Args, Res>(
        &mut self,
        op: &mut dyn PointOperation<Node, Args, Res>,
        args: Args,
    ) -> Res {
        assert_ne!(self.n, 0);
        self.do_point_operation(op, self.nodes.len() - 1, 0, self.n, args)
    }

    fn do_point_operation<Args, Res>(
        &mut self,
        op: &mut dyn PointOperation<Node, Args, Res>,
        root: usize,
        left: usize,
        right: usize,
        args: Args,
    ) -> Res {
        if left + 1 == right {
            op.adjust_leaf(&mut self.nodes[root], left, args)
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            let (l, r) = self.nodes.split_at_mut(root);
            let (l, m) = l.split_at_mut(right_child);
            let direction = op.select_branch(
                &mut r[0],
                &mut l[left_child],
                &mut m[0],
                &args,
                left,
                mid,
                right,
            );
            let res = match direction {
                Direction::Left => self.do_point_operation(op, left_child, left, mid, args),
                Direction::Right => self.do_point_operation(op, right_child, mid, right, args),
            };
            self.join(root, mid, right);
            res
        }
    }

    pub fn update<'a, T>(&mut self, range: impl RangeBounds<usize>, val: &'a T)
    where
        Node: Pushable<&'a T>,
    {
        let (from, to) = clamp(range, self.n);
        self.do_update(self.nodes.len() - 1, 0, self.n, from, to, val)
    }

    pub fn do_update<'a, T>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        from: usize,
        to: usize,
        val: &'a T,
    ) where
        Node: Pushable<&'a T>,
    {
        when! {
            left >= to || right <= from => {},
            left >= from && right <= to => self.nodes[root].push(val),
            else => {
                let mid = (left + right) >> 1;
                self.push_down(root, mid, right);
                let left_child = root - 2 * (right - mid);
                let right_child = root - 1;
                self.do_update(left_child, left, mid, from, to, val);
                self.do_update(right_child, mid, right, from, to, val);
                self.join(root, mid, right);
            },
        }
    }

    pub fn operation<Args, Res>(
        &mut self,
        range: impl RangeBounds<usize>,
        op: &mut dyn Operation<Node, Args, Res>,
        args: &Args,
    ) -> Res {
        let (from, to) = clamp(range, self.n);
        self.do_operation(self.nodes.len() - 1, 0, self.n, from, to, op, args)
    }

    pub fn do_operation<Args, Res>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        from: usize,
        to: usize,
        op: &mut dyn Operation<Node, Args, Res>,
        args: &Args,
    ) -> Res {
        when! {
            left >= to || right <= from => op.empty_result(left, right, args),
            left >= from && right <= to => op.process_result(&mut self.nodes[root], args),
            else => {
                let mid = (left + right) >> 1;
                self.push_down(root, mid, right);
                let left_child = root - 2 * (right - mid);
                let right_child = root - 1;
                let left_result = self.do_operation(left_child, left, mid, from, to, op, args);
                let right_result = self.do_operation(right_child, mid, right, from, to, op, args);
                self.join(root, mid, right);
                op.join_results(left_result, right_result, args)
            },
        }
    }

    pub fn binary_search<Res>(
        &mut self,
        wh: impl FnMut(&Node, &Node) -> Direction,
        calc: impl FnMut(&Node, usize) -> Res,
    ) -> Res {
        self.do_binary_search(self.nodes.len() - 1, 0, self.n, wh, calc)
    }

    fn do_binary_search<Res>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        mut wh: impl FnMut(&Node, &Node) -> Direction,
        mut calc: impl FnMut(&Node, usize) -> Res,
    ) -> Res {
        if left + 1 == right {
            calc(&self.nodes[root], left)
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            let direction = wh(&self.nodes[left_child], &self.nodes[right_child]);
            match direction {
                Direction::Left => self.do_binary_search(left_child, left, mid, wh, calc),
                Direction::Right => self.do_binary_search(right_child, mid, right, wh, calc),
            }
        }
    }

    fn join(&mut self, root: usize, mid: usize, right: usize) {
        let left_child = root - 2 * (right - mid);
        let right_child = root - 1;
        let (left_node, right_node) = self.nodes.split_at_mut(root);
        right_node[0].join(&left_node[left_child], &left_node[right_child]);
    }

    fn do_push_down(&mut self, parent: usize, to: usize) {
        let (left_nodes, right_nodes) = self.nodes.split_at_mut(parent);
        left_nodes[to].accumulate(&right_nodes[0]);
    }

    fn push_down(&mut self, root: usize, mid: usize, right: usize) {
        self.do_push_down(root, root - 2 * (right - mid));
        self.do_push_down(root, root - 1);
        self.nodes[root].reset_delta();
    }

    pub fn query<T>(&mut self, range: impl RangeBounds<usize>) -> T
    where
        Node: QueryResult<T, ()>,
    {
        let (from, to) = clamp(range, self.n);
        if from >= to {
            Node::empty_result(&())
        } else {
            self.do_query(self.nodes.len() - 1, 0, self.n, from, to, &())
        }
    }

    pub fn query_with_args<T, Args>(&mut self, range: impl RangeBounds<usize>, args: &Args) -> T
    where
        Node: QueryResult<T, Args>,
    {
        let (from, to) = clamp(range, self.n);
        if from >= to {
            Node::empty_result(args)
        } else {
            self.do_query(self.nodes.len() - 1, 0, self.n, from, to, args)
        }
    }

    fn do_query<T, Args>(
        &mut self,
        root: usize,
        left: usize,
        right: usize,
        from: usize,
        to: usize,
        args: &Args,
    ) -> T
    where
        Node: QueryResult<T, Args>,
    {
        if left >= from && right <= to {
            self.nodes[root].result(args)
        } else {
            let mid = (left + right) >> 1;
            self.push_down(root, mid, right);
            let left_child = root - 2 * (right - mid);
            let right_child = root - 1;
            when! {
                to <= mid => self.do_query(left_child, left, mid, from, to, args),
                from >= mid => self.do_query(right_child, mid, right, from, to, args),
                else => {
                    let left_result = self.do_query(left_child, left, mid, from, to, args);
                    let right_result = self.do_query(right_child, mid, right, from, to, args);
                    Node::join_results(left_result, right_result, args, left, mid, right)
                },
            }
        }
    }
}

pub trait PointOperation<Node: SegmentTreeNode, Args, Res = Node> {
    fn adjust_leaf(&mut self, leaf: &mut Node, at: usize, args: Args) -> Res;
    fn select_branch(
        &mut self,
        root: &mut Node,
        left_child: &mut Node,
        right_child: &mut Node,
        args: &Args,
        left: usize,
        mid: usize,
        right: usize,
    ) -> Direction;
}

pub struct PointOperationClosure<'s, Node: SegmentTreeNode, Args, Res = Node> {
    adjust_leaf: Box<dyn FnMut(&mut Node, usize, Args) -> Res + 's>,
    select_branch: Box<
        dyn FnMut(&mut Node, &mut Node, &mut Node, &Args, usize, usize, usize) -> Direction + 's,
    >,
    phantom_node: PhantomData<Node>,
    phantom_args: PhantomData<Args>,
    phantom_res: PhantomData<Res>,
}

impl<'s, Node: SegmentTreeNode, Args, Res> PointOperationClosure<'s, Node, Args, Res> {
    pub fn new<F1, F2>(adjust_leaf: F1, select_branch: F2) -> Self
    where
        F1: FnMut(&mut Node, usize, Args) -> Res + 's,
        F2: FnMut(&mut Node, &mut Node, &mut Node, &Args, usize, usize, usize) -> Direction + 's,
    {
        Self {
            adjust_leaf: Box::new(adjust_leaf),
            select_branch: Box::new(select_branch),
            phantom_node: Default::default(),
            phantom_args: Default::default(),
            phantom_res: Default::default(),
        }
    }
}

impl<'s, Node: SegmentTreeNode, Args, Res> PointOperation<Node, Args, Res>
    for PointOperationClosure<'s, Node, Args, Res>
{
    fn adjust_leaf(&mut self, leaf: &mut Node, at: usize, args: Args) -> Res {
        (self.adjust_leaf)(leaf, at, args)
    }

    fn select_branch(
        &mut self,
        root: &mut Node,
        left_child: &mut Node,
        right_child: &mut Node,
        args: &Args,
        left: usize,
        mid: usize,
        right: usize,
    ) -> Direction {
        (self.select_branch)(root, left_child, right_child, args, left, mid, right)
    }
}

pub trait Operation<Node: SegmentTreeNode, Args, Res = Node> {
    fn process_result(&mut self, node: &mut Node, args: &Args) -> Res;
    fn join_results(&mut self, left_res: Res, right_res: Res, args: &Args) -> Res;
    fn empty_result(&mut self, left: usize, right: usize, args: &Args) -> Res;
}

pub struct OperationClosure<'s, Node: SegmentTreeNode, Args, Res = Node> {
    process_result: Box<dyn FnMut(&mut Node, &Args) -> Res + 's>,
    join_results: Box<dyn FnMut(Res, Res, &Args) -> Res + 's>,
    empty_result: Box<dyn FnMut(usize, usize, &Args) -> Res + 's>,
    phantom_node: PhantomData<Node>,
    phantom_args: PhantomData<Args>,
    phantom_res: PhantomData<Res>,
}

impl<'s, Node: SegmentTreeNode, Args, Res> OperationClosure<'s, Node, Args, Res> {
    pub fn new<F1, F2, F3>(process_result: F1, join_results: F2, empty_result: F3) -> Self
    where
        F1: FnMut(&mut Node, &Args) -> Res + 's,
        F2: FnMut(Res, Res, &Args) -> Res + 's,
        F3: FnMut(usize, usize, &Args) -> Res + 's,
    {
        Self {
            process_result: Box::new(process_result),
            join_results: Box::new(join_results),
            empty_result: Box::new(empty_result),
            phantom_node: Default::default(),
            phantom_args: Default::default(),
            phantom_res: Default::default(),
        }
    }
}

impl<'s, Node: SegmentTreeNode, Args, Res> Operation<Node, Args, Res>
    for OperationClosure<'s, Node, Args, Res>
{
    fn process_result(&mut self, node: &mut Node, args: &Args) -> Res {
        (self.process_result)(node, args)
    }

    fn join_results(&mut self, left_res: Res, right_res: Res, args: &Args) -> Res {
        (self.join_results)(left_res, right_res, args)
    }

    fn empty_result(&mut self, left: usize, right: usize, args: &Args) -> Res {
        (self.empty_result)(left, right, args)
    }
}
}
pub mod slice_ext {
pub mod backward {
use std::ops::Index;
use std::ops::IndexMut;

pub struct Back(pub usize);

impl<T> Index<Back> for [T] {
    type Output = T;

    fn index(&self, index: Back) -> &Self::Output {
        &self[self.len() - index.0 - 1]
    }
}

impl<T> IndexMut<Back> for [T] {
    fn index_mut(&mut self, index: Back) -> &mut Self::Output {
        &mut self[self.len() - index.0 - 1]
    }
}

impl<T> Index<Back> for Vec<T> {
    type Output = T;

    fn index(&self, index: Back) -> &Self::Output {
        self.as_slice().index(index)
    }
}

impl<T> IndexMut<Back> for Vec<T> {
    fn index_mut(&mut self, index: Back) -> &mut Self::Output {
        self.as_mut_slice().index_mut(index)
    }
}
}
pub mod bounds {
pub trait Bounds<T: PartialOrd> {
    fn lower_bound(&self, el: &T) -> usize;
    fn upper_bound(&self, el: &T) -> usize;
    fn bin_search(&self, el: &T) -> Option<usize>;
    fn more(&self, el: &T) -> usize;
    fn more_or_eq(&self, el: &T) -> usize;
    fn less(&self, el: &T) -> usize;
    fn less_or_eq(&self, el: &T) -> usize;
}

impl<T: PartialOrd> Bounds<T> for [T] {
    fn lower_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] < el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }

    fn upper_bound(&self, el: &T) -> usize {
        let mut left = 0;
        let mut right = self.len();
        while left < right {
            let mid = left + ((right - left) >> 1);
            if &self[mid] <= el {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        left
    }

    fn bin_search(&self, el: &T) -> Option<usize> {
        let at = self.lower_bound(el);
        if at == self.len() || &self[at] != el {
            None
        } else {
            Some(at)
        }
    }

    fn more(&self, el: &T) -> usize {
        self.len() - self.upper_bound(el)
    }

    fn more_or_eq(&self, el: &T) -> usize {
        self.len() - self.lower_bound(el)
    }

    fn less(&self, el: &T) -> usize {
        self.lower_bound(el)
    }

    fn less_or_eq(&self, el: &T) -> usize {
        self.upper_bound(el)
    }
}
}
pub mod compress {
use crate::algo_lib::collections::slice_ext::bounds::Bounds;
use std::mem::MaybeUninit;

#[derive(Eq, PartialEq, Debug)]
pub struct Compressed<T, const N: usize> {
    pub order: Vec<T>,
    pub arrs: [Vec<usize>; N],
}

pub fn compress<T: Ord + Clone, const N: usize>(vs: [&[T]; N]) -> Compressed<T, N> {
    let mut size = 0;
    for v in &vs {
        size += v.len();
    }
    let mut all = Vec::with_capacity(size);
    for v in &vs {
        all.extend_from_slice(v);
    }
    all.sort();
    all.dedup();
    let arrs = unsafe {
        let mut arr: MaybeUninit<[Vec<usize>; N]> = MaybeUninit::uninit();
        for (i, v) in vs.iter().enumerate() {
            let mut cur = Vec::with_capacity(vs[i].len());
            for vv in *v {
                cur.push(all.bin_search(vv).unwrap());
            }
            arr.as_mut_ptr().cast::<Vec<usize>>().add(i).write(cur);
        }
        arr.assume_init()
    };
    Compressed { order: all, arrs }
}
}
pub mod indices {
use std::ops::Range;

pub trait Indices {
    fn indices(&self) -> Range<usize>;
}

impl<T> Indices for [T] {
    fn indices(&self) -> Range<usize> {
        0..self.len()
    }
}
}
}
pub mod vec_ext {
pub mod default {
pub fn default_vec<T: Default>(len: usize) -> Vec<T> {
    let mut v = Vec::with_capacity(len);
    for _ in 0..len {
        v.push(T::default());
    }
    v
}
}
}
}
pub mod io {
pub mod input {
use crate::algo_lib::collections::vec_ext::default::default_vec;
use std::io::Read;
use std::mem::MaybeUninit;

pub struct Input<'s> {
    input: &'s mut (dyn Read + Send),
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
}

macro_rules! read_impl {
    ($t: ty, $read_name: ident, $read_vec_name: ident) => {
        pub fn $read_name(&mut self) -> $t {
            self.read()
        }

        pub fn $read_vec_name(&mut self, len: usize) -> Vec<$t> {
            self.read_vec(len)
        }
    };

    ($t: ty, $read_name: ident, $read_vec_name: ident, $read_pair_vec_name: ident) => {
        read_impl!($t, $read_name, $read_vec_name);

        pub fn $read_pair_vec_name(&mut self, len: usize) -> Vec<($t, $t)> {
            self.read_vec(len)
        }
    };
}

impl<'s> Input<'s> {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(input: &'s mut (dyn Read + Send)) -> Self {
        Self {
            input,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_with_size(input: &'s mut (dyn Read + Send), buf_size: usize) -> Self {
        Self {
            input,
            buf: default_vec(buf_size),
            at: 0,
            buf_read: 0,
        }
    }

    pub fn get(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            self.at += 1;
            if res == b'\r' {
                if self.refill_buffer() && self.buf[self.at] == b'\n' {
                    self.at += 1;
                }
                return Some(b'\n');
            }
            Some(res)
        } else {
            None
        }
    }

    pub fn peek(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            Some(if res == b'\r' { b'\n' } else { res })
        } else {
            None
        }
    }

    pub fn skip_whitespace(&mut self) {
        while let Some(b) = self.peek() {
            if !b.is_ascii_whitespace() {
                return;
            }
            self.get();
        }
    }

    pub fn next_token(&mut self) -> Option<Vec<u8>> {
        self.skip_whitespace();
        let mut res = Vec::new();
        while let Some(c) = self.get() {
            if c.is_ascii_whitespace() {
                break;
            }
            res.push(c);
        }
        if res.is_empty() {
            None
        } else {
            Some(res)
        }
    }

    //noinspection RsSelfConvention
    pub fn is_exhausted(&mut self) -> bool {
        self.peek().is_none()
    }

    //noinspection RsSelfConvention
    pub fn is_empty(&mut self) -> bool {
        self.skip_whitespace();
        self.is_exhausted()
    }

    pub fn read<T: Readable>(&mut self) -> T {
        T::read(self)
    }

    pub fn read_vec<T: Readable>(&mut self, size: usize) -> Vec<T> {
        let mut res = Vec::with_capacity(size);
        for _ in 0..size {
            res.push(self.read());
        }
        res
    }

    pub fn read_char(&mut self) -> u8 {
        self.skip_whitespace();
        self.get().unwrap()
    }

    read_impl!(u32, read_unsigned, read_unsigned_vec);
    read_impl!(u64, read_u64, read_u64_vec);
    read_impl!(usize, read_size, read_size_vec, read_size_pair_vec);
    read_impl!(i32, read_int, read_int_vec, read_int_pair_vec);
    read_impl!(i64, read_long, read_long_vec, read_long_pair_vec);
    read_impl!(i128, read_i128, read_i128_vec);

    fn refill_buffer(&mut self) -> bool {
        if self.at == self.buf_read {
            self.at = 0;
            self.buf_read = self.input.read(&mut self.buf).unwrap();
            self.buf_read != 0
        } else {
            true
        }
    }
}

pub trait Readable {
    fn read(input: &mut Input) -> Self;
}

impl Readable for u8 {
    fn read(input: &mut Input) -> Self {
        input.read_char()
    }
}

impl<T: Readable> Readable for Vec<T> {
    fn read(input: &mut Input) -> Self {
        let size = input.read();
        input.read_vec(size)
    }
}

impl<T: Readable, const SIZE: usize> Readable for [T; SIZE] {
    fn read(input: &mut Input) -> Self {
        unsafe {
            let mut res = MaybeUninit::<[T; SIZE]>::uninit();
            for i in 0..SIZE {
                let ptr: *mut T = (*res.as_mut_ptr()).as_mut_ptr();
                ptr.add(i).write(input.read::<T>());
            }
            res.assume_init()
        }
    }
}

macro_rules! read_integer {
    ($($t:ident)+) => {$(
        impl Readable for $t {
            fn read(input: &mut Input) -> Self {
                input.skip_whitespace();
                let mut c = input.get().unwrap();
                let sgn = match c {
                    b'-' => {
                        c = input.get().unwrap();
                        true
                    }
                    b'+' => {
                        c = input.get().unwrap();
                        false
                    }
                    _ => false,
                };
                let mut res = 0;
                loop {
                    assert!(c.is_ascii_digit());
                    res *= 10;
                    let d = (c - b'0') as $t;
                    if sgn {
                        res -= d;
                    } else {
                        res += d;
                    }
                    match input.get() {
                        None => break,
                        Some(ch) => {
                            if ch.is_ascii_whitespace() {
                                break;
                            } else {
                                c = ch;
                            }
                        }
                    }
                }
                res
            }
        }
    )+};
}

read_integer!(i8 i16 i32 i64 i128 isize u16 u32 u64 u128 usize);

macro_rules! tuple_readable {
    ($($name:ident)+) => {
        impl<$($name: Readable), +> Readable for ($($name,)+) {
            fn read(input: &mut Input) -> Self {
                ($($name::read(input),)+)
            }
        }
    }
}

tuple_readable! {T}
tuple_readable! {T U}
tuple_readable! {T U V}
tuple_readable! {T U V X}
tuple_readable! {T U V X Y}
tuple_readable! {T U V X Y Z}
tuple_readable! {T U V X Y Z A}
tuple_readable! {T U V X Y Z A B}
tuple_readable! {T U V X Y Z A B C}
tuple_readable! {T U V X Y Z A B C D}
tuple_readable! {T U V X Y Z A B C D E}
tuple_readable! {T U V X Y Z A B C D E F}

impl Read for Input<'_> {
    fn read(&mut self, buf: &mut [u8]) -> std::io::Result<usize> {
        if self.at == self.buf_read {
            self.input.read(buf)
        } else {
            let mut i = 0;
            while i < buf.len() && self.at < self.buf_read {
                buf[i] = self.buf[self.at];
                i += 1;
                self.at += 1;
            }
            Ok(i)
        }
    }
}
}
pub mod output {
use crate::algo_lib::collections::vec_ext::default::default_vec;
use std::cmp::Reverse;
use std::io::stderr;
use std::io::Stderr;
use std::io::Write;

#[derive(Copy, Clone)]
pub enum BoolOutput {
    YesNo,
    YesNoCaps,
    PossibleImpossible,
    Custom(&'static str, &'static str),
}

impl BoolOutput {
    pub fn output(&self, output: &mut Output, val: bool) {
        (if val { self.yes() } else { self.no() }).write(output);
    }

    fn yes(&self) -> &str {
        match self {
            BoolOutput::YesNo => "Yes",
            BoolOutput::YesNoCaps => "YES",
            BoolOutput::PossibleImpossible => "Possible",
            BoolOutput::Custom(yes, _) => yes,
        }
    }

    fn no(&self) -> &str {
        match self {
            BoolOutput::YesNo => "No",
            BoolOutput::YesNoCaps => "NO",
            BoolOutput::PossibleImpossible => "Impossible",
            BoolOutput::Custom(_, no) => no,
        }
    }
}

pub struct Output<'s> {
    output: &'s mut dyn Write,
    buf: Vec<u8>,
    at: usize,
    auto_flush: bool,
    bool_output: BoolOutput,
    precision: Option<usize>,
}

impl<'s> Output<'s> {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(output: &'s mut dyn Write) -> Self {
        Self {
            output,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            auto_flush: false,
            bool_output: BoolOutput::YesNoCaps,
            precision: None,
        }
    }

    pub fn new_with_auto_flush(output: &'s mut dyn Write) -> Self {
        Self {
            output,
            buf: default_vec(Self::DEFAULT_BUF_SIZE),
            at: 0,
            auto_flush: true,
            bool_output: BoolOutput::YesNoCaps,
            precision: None,
        }
    }

    pub fn flush(&mut self) {
        if self.at != 0 {
            self.output.write_all(&self.buf[..self.at]).unwrap();
            self.output.flush().unwrap();
            self.at = 0;
        }
    }

    pub fn print<T: Writable>(&mut self, s: T) {
        s.write(self);
        self.maybe_flush();
    }

    pub fn print_line<T: Writable>(&mut self, s: T) {
        self.print(s);
        self.put(b'\n');
        self.maybe_flush();
    }

    pub fn put(&mut self, b: u8) {
        self.buf[self.at] = b;
        self.at += 1;
        if self.at == self.buf.len() {
            self.flush();
        }
    }

    pub fn maybe_flush(&mut self) {
        if self.auto_flush {
            self.flush();
        }
    }

    pub fn print_per_line<T: Writable>(&mut self, arg: &[T]) {
        self.print_per_line_iter(arg.iter());
    }

    pub fn print_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        let mut first = true;
        for e in iter {
            if first {
                first = false;
            } else {
                self.put(b' ');
            }
            e.write(self);
        }
    }

    pub fn print_line_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        self.print_iter(iter);
        self.put(b'\n');
    }

    pub fn print_per_line_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        for e in iter {
            e.write(self);
            self.put(b'\n');
        }
    }

    pub fn set_bool_output(&mut self, bool_output: BoolOutput) {
        self.bool_output = bool_output;
    }
    pub fn set_precision(&mut self, precision: usize) {
        self.precision = Some(precision);
    }
    pub fn reset_precision(&mut self) {
        self.precision = None;
    }
    pub fn get_precision(&self) -> Option<usize> {
        self.precision
    }
}

impl Write for Output<'_> {
    fn write(&mut self, buf: &[u8]) -> std::io::Result<usize> {
        let mut start = 0usize;
        let mut rem = buf.len();
        while rem > 0 {
            let len = (self.buf.len() - self.at).min(rem);
            self.buf[self.at..self.at + len].copy_from_slice(&buf[start..start + len]);
            self.at += len;
            if self.at == self.buf.len() {
                self.flush();
            }
            start += len;
            rem -= len;
        }
        self.maybe_flush();
        Ok(buf.len())
    }

    fn flush(&mut self) -> std::io::Result<()> {
        self.flush();
        Ok(())
    }
}

pub trait Writable {
    fn write(&self, output: &mut Output);
}

impl Writable for &str {
    fn write(&self, output: &mut Output) {
        output.write_all(self.as_bytes()).unwrap();
    }
}

impl Writable for String {
    fn write(&self, output: &mut Output) {
        output.write_all(self.as_bytes()).unwrap();
    }
}

impl Writable for char {
    fn write(&self, output: &mut Output) {
        output.put(*self as u8);
    }
}

impl Writable for u8 {
    fn write(&self, output: &mut Output) {
        output.put(*self);
    }
}

impl<T: Writable> Writable for [T] {
    fn write(&self, output: &mut Output) {
        output.print_iter(self.iter());
    }
}

impl<T: Writable, const N: usize> Writable for [T; N] {
    fn write(&self, output: &mut Output) {
        output.print_iter(self.iter());
    }
}

impl<T: Writable + ?Sized> Writable for &T {
    fn write(&self, output: &mut Output) {
        T::write(self, output)
    }
}

impl<T: Writable> Writable for Vec<T> {
    fn write(&self, output: &mut Output) {
        self.as_slice().write(output);
    }
}

impl Writable for () {
    fn write(&self, _output: &mut Output) {}
}

macro_rules! write_to_string {
    ($($t:ident)+) => {$(
        impl Writable for $t {
            fn write(&self, output: &mut Output) {
                self.to_string().write(output);
            }
        }
    )+};
}

write_to_string!(u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);

macro_rules! tuple_writable {
    ($name0:ident $($name:ident: $id:tt )*) => {
        impl<$name0: Writable, $($name: Writable,)*> Writable for ($name0, $($name,)*) {
            fn write(&self, out: &mut Output) {
                self.0.write(out);
                $(
                out.put(b' ');
                self.$id.write(out);
                )*
            }
        }
    }
}

tuple_writable! {T}
tuple_writable! {T U:1}
tuple_writable! {T U:1 V:2}
tuple_writable! {T U:1 V:2 X:3}
tuple_writable! {T U:1 V:2 X:3 Y:4}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6 B:7}
tuple_writable! {T U:1 V:2 X:3 Y:4 Z:5 A:6 B:7 C:8}

impl<T: Writable> Writable for Option<T> {
    fn write(&self, output: &mut Output) {
        match self {
            None => (-1).write(output),
            Some(t) => t.write(output),
        }
    }
}

impl Writable for bool {
    fn write(&self, output: &mut Output) {
        let bool_output = output.bool_output;
        bool_output.output(output, *self)
    }
}

impl<T: Writable> Writable for Reverse<T> {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
    }
}

static mut ERR: Option<Stderr> = None;

pub fn err() -> Output<'static> {
    unsafe {
        if ERR.is_none() {
            ERR = Some(stderr());
        }
        Output::new_with_auto_flush(ERR.as_mut().unwrap())
    }
}
}
}
pub mod misc {
pub mod direction {
#[derive(Copy, Clone)]
pub enum Direction {
    Left,
    Right,
}
}
pub mod test_type {
pub enum TestType {
    Single,
    MultiNumber,
    MultiEof,
}

pub enum TaskType {
    Classic,
    Interactive,
}
}
pub mod when {
#[macro_export]
macro_rules! when {
    {$($cond: expr => $then: expr,)*} => {
        match () {
            $(_ if $cond => $then,)*
            _ => unreachable!(),
        }
    };
    {$($cond: expr => $then: expr,)* else $(=>)? $else: expr$(,)?} => {
        match () {
            $(_ if $cond => $then,)*
            _ => $else,
        }
    };
}
}
}
pub mod numbers {
pub mod num_traits {
pub mod algebra {
use crate::algo_lib::numbers::num_traits::invertible::Invertible;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Neg;
use std::ops::Rem;
use std::ops::RemAssign;
use std::ops::Sub;
use std::ops::SubAssign;

pub trait Zero {
    fn zero() -> Self;
}

pub trait One {
    fn one() -> Self;
}

pub trait AdditionMonoid: Add<Output = Self> + AddAssign + Zero + Eq + Sized {}

impl<T: Add<Output = Self> + AddAssign + Zero + Eq> AdditionMonoid for T {}

pub trait AdditionMonoidWithSub: AdditionMonoid + Sub<Output = Self> + SubAssign {}

impl<T: AdditionMonoid + Sub<Output = Self> + SubAssign> AdditionMonoidWithSub for T {}

pub trait AdditionGroup: AdditionMonoidWithSub + Neg<Output = Self> {}

impl<T: AdditionMonoidWithSub + Neg<Output = Self>> AdditionGroup for T {}

pub trait MultiplicationMonoid: Mul<Output = Self> + MulAssign + One + Eq + Sized {}

impl<T: Mul<Output = Self> + MulAssign + One + Eq> MultiplicationMonoid for T {}

pub trait IntegerMultiplicationMonoid:
    MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign + RemAssign
{
}

impl<T: MultiplicationMonoid + Div<Output = Self> + Rem<Output = Self> + DivAssign + RemAssign>
    IntegerMultiplicationMonoid for T
{
}

pub trait MultiplicationGroup:
    MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>
{
}

impl<T: MultiplicationMonoid + Div<Output = Self> + DivAssign + Invertible<Output = Self>>
    MultiplicationGroup for T
{
}

pub trait SemiRing: AdditionMonoid + MultiplicationMonoid {}

impl<T: AdditionMonoid + MultiplicationMonoid> SemiRing for T {}

pub trait SemiRingWithSub: AdditionMonoidWithSub + SemiRing {}

impl<T: AdditionMonoidWithSub + SemiRing> SemiRingWithSub for T {}

pub trait Ring: SemiRing + AdditionGroup {}

impl<T: SemiRing + AdditionGroup> Ring for T {}

pub trait IntegerSemiRing: SemiRing + IntegerMultiplicationMonoid {}

impl<T: SemiRing + IntegerMultiplicationMonoid> IntegerSemiRing for T {}

pub trait IntegerSemiRingWithSub: SemiRingWithSub + IntegerSemiRing {}

impl<T: SemiRingWithSub + IntegerSemiRing> IntegerSemiRingWithSub for T {}

pub trait IntegerRing: IntegerSemiRing + Ring {}

impl<T: IntegerSemiRing + Ring> IntegerRing for T {}

pub trait Field: Ring + MultiplicationGroup {}

impl<T: Ring + MultiplicationGroup> Field for T {}

macro_rules! zero_one_integer_impl {
    ($($t: ident)+) => {$(
        impl Zero for $t {
            fn zero() -> Self {
                0
            }
        }

        impl One for $t {
            fn one() -> Self {
                1
            }
        }
    )+};
}

zero_one_integer_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod as_index {
pub trait AsIndex {
    fn from_index(idx: usize) -> Self;
    fn to_index(self) -> usize;
}

macro_rules! from_index_impl {
    ($($t: ident)+) => {$(
        impl AsIndex for $t {
            fn from_index(idx: usize) -> Self {
                idx as $t
            }

            fn to_index(self) -> usize {
                self as usize
            }
        }
    )+};
}

from_index_impl!(i128 i64 i32 i16 i8 isize u128 u64 u32 u16 u8 usize);
}
pub mod invertible {
pub trait Invertible {
    type Output;

    fn inv(&self) -> Option<Self::Output>;
}
}
}
pub mod num_utils {
use crate::algo_lib::numbers::num_traits::algebra::AdditionMonoid;
use crate::algo_lib::numbers::num_traits::algebra::IntegerRing;
use crate::algo_lib::numbers::num_traits::algebra::MultiplicationMonoid;
use crate::algo_lib::numbers::num_traits::as_index::AsIndex;

pub fn factorials<T: MultiplicationMonoid + Copy + AsIndex>(len: usize) -> Vec<T> {
    let mut res = Vec::new();
    if len > 0 {
        res.push(T::one());
    }
    while res.len() < len {
        res.push((*res.last().unwrap()) * T::from_index(res.len()));
    }
    res
}

pub fn powers<T: MultiplicationMonoid + Copy>(base: T, len: usize) -> Vec<T> {
    let mut res = Vec::new();
    if len > 0 {
        res.push(T::one());
    }
    while res.len() < len {
        res.push((*res.last().unwrap()) * base);
    }
    res
}

pub struct Powers<T: MultiplicationMonoid + Copy> {
    small: Vec<T>,
    big: Vec<T>,
}

impl<T: MultiplicationMonoid + Copy> Powers<T> {
    pub fn new(base: T, len: usize) -> Self {
        let small = powers(base, len);
        let big = powers(small[len - 1] * base, len);
        Self { small, big }
    }

    pub fn power(&self, exp: usize) -> T {
        debug_assert!(exp < self.small.len() * self.small.len());
        self.big[exp / self.small.len()] * self.small[exp % self.small.len()]
    }
}

pub fn factorial<T: MultiplicationMonoid + AsIndex>(n: usize) -> T {
    let mut res = T::one();
    for i in 1..=n {
        res *= T::from_index(i);
    }
    res
}

pub trait PartialSums<T> {
    fn partial_sums(&self) -> Vec<T>;
}

impl<T: AdditionMonoid + Copy> PartialSums<T> for [T] {
    fn partial_sums(&self) -> Vec<T> {
        let mut res = Vec::with_capacity(self.len() + 1);
        res.push(T::zero());
        for i in self.iter() {
            res.push(*res.last().unwrap() + *i);
        }
        res
    }
}

pub trait UpperDiv {
    fn upper_div(self, other: Self) -> Self;
}

impl<T: IntegerRing + Copy> UpperDiv for T {
    fn upper_div(self, other: Self) -> Self {
        (self + other - Self::one()) / other
    }
}
}
}
}
fn main() {
    let mut sin = std::io::stdin();
    let input = algo_lib::io::input::Input::new(&mut sin);
    let mut stdout = std::io::stdout();
    let output = algo_lib::io::output::Output::new(&mut stdout);
    solution::run(input, output);
}