// 
pub mod solution {
//{"name":"a","group":"Manual","url":"","interactive":false,"timeLimit":2000,"tests":[{"input":"","output":""}],"testType":"single","input":{"type":"stdin","fileName":null,"pattern":null},"output":{"type":"stdout","fileName":null,"pattern":null},"languages":{"java":{"taskClass":"a"}}}

use std::vec;

#[allow(unused)]
use crate::dbg;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::math::modulo::Mod9;
use crate::algo_lib::misc::binary_search::binary_search_last_true;
use crate::algo_lib::seg_trees::lazy_seg_tree::SegTree;
use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;

type Mod = Mod9;

pub struct Context {
    powers: Vec<Mod>,
    #[allow(unused)]
    multiplier: Mod,
}

impl Context {
    pub fn new(max_len: usize, multiplier: Mod) -> Self {
        let mut powers = Vec::with_capacity(max_len + 1);
        powers.push(Mod::ONE);
        for i in 1..=max_len {
            powers.push(powers[i - 1] * multiplier);
        }
        Self { powers, multiplier }
    }
}

#[derive(Copy, Clone, Default)]
pub struct Node {
    hash: Mod,
    hash_rev: Mod,
    size: usize,
}

impl Node {
    pub fn new(hash: Mod) -> Self {
        Self {
            hash,
            hash_rev: hash,
            size: 1,
        }
    }
}

impl SegTreeNode for Node {
    fn join_nodes(lhs: &Self, rhs: &Self, ctx: &Self::Context) -> Self {
        Self {
            hash: lhs.hash * ctx.powers[rhs.size] + rhs.hash,
            hash_rev: rhs.hash_rev * ctx.powers[lhs.size] + lhs.hash_rev,
            size: lhs.size + rhs.size,
        }
    }

    fn apply_update(node: &mut Self, update: &Self::Update) {
        todo!()
    }

    fn join_updates(current: &mut Self::Update, add: &Self::Update) {
        todo!()
    }

    type Update = ();

    type Context = Context;
}

fn solve(input: &mut Input, out: &mut Output, _test_case: usize) {
    let n = input.usize();
    let q = input.usize();
    let k = Mod::new(input.i32());
    let b = Mod::new(input.i32());
    let a = input.vec::<i32>(n);
    let mut deltas = vec![Mod::ZERO; n - 1];
    for i in 0..n - 1 {
        deltas[i] = Mod::new(a[i + 1] - a[i]);
    }
    let multiplier = Mod::new(2390171);
    let context = Context::new(n + 1, multiplier);
    let mut deltas_seg_tree = SegTree::new_with_context(
        n,
        |i| {
            if i == n - 1 {
                Node::new(Mod::ZERO)
            } else {
                Node::new(deltas[i])
            }
        },
        context,
    );
    let mut expected_hashes = vec![Mod::ZERO; n + 1];
    for len in 1..=n {
        expected_hashes[len] = expected_hashes[len - 1] * multiplier + k;
    }

    for _ in 0..q {
        let q_type = input.usize();
        if q_type == 1 {
            let l = input.usize() - 1;
            let r = input.usize() - 1;
            let v = Mod::new(input.i32());
            if l != 0 {
                deltas[l - 1] += v;
                deltas_seg_tree.update_point(l - 1, Node::new(deltas[l - 1]));
            }
            if r != n - 1 {
                deltas[r] -= v;
                deltas_seg_tree.update_point(r, Node::new(deltas[r]));
            }
        } else {
            assert_eq!(q_type, 2);
            let mid = input.usize() - 1;
            let res = {
                if mid == 0 || mid == n - 1 {
                    0
                } else {
                    let expected = k + b;
                    let real = deltas[mid - 1] + deltas[mid];
                    if expected != real {
                        0
                    } else {
                        binary_search_last_true(1..(mid + 1).max(n - mid) - 1, |check| {
                            let len = check - 1;
                            // dbg!(mid, len);
                            let to1 = mid - 1;
                            let from1 = to1 + 1 - len;
                            let from2 = mid + 1;
                            let to2 = from2 + len;
                            // dbg!("Checking", mid, len, from1, to1, from2, to2);
                            assert!(to2 < n);
                            let hash = deltas_seg_tree.get(from1..from1 + len).hash
                                + deltas_seg_tree.get(from2..from2 + len).hash_rev;
                            let expected_hash = expected_hashes[len];
                            hash == expected_hash
                            // for i in 0..len {
                            //     let ss = deltas[from1 + i] + deltas[to2 - 1 - i];
                            //     if ss != k {
                            //         return false;
                            //     }
                            // }
                            // true
                        })
                        .unwrap()
                        // let mut r = 1;
                        // loop {
                        //     if mid - r == 0 || mid + r == n - 1 {
                        //         break;
                        //     }
                        //     let sum_deltas = deltas[mid - r - 1] + deltas[mid + r];
                        //     if sum_deltas != k {
                        //         break;
                        //     } else {
                        //         r += 1;
                        //     }
                        // }
                        // r
                    }
                }
            };
            out.println(res);
        }
    }
}

pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    solve(&mut input, &mut output, 1);
    output.flush();
    true
}

}
pub mod algo_lib {
pub mod collections {
pub mod last_exn {
use std::collections::BTreeSet;

pub trait LastExn<T> {
    fn last_exn(&self) -> &T;
}

impl<T> LastExn<T> for &[T] {
    fn last_exn(&self) -> &T {
        self.last().unwrap()
    }
}

impl<T> LastExn<T> for Vec<T> {
    fn last_exn(&self) -> &T {
        self.last().unwrap()
    }
}

impl<T> LastExn<T> for BTreeSet<T> {
    fn last_exn(&self) -> &T {
        self.iter().next_back().unwrap()
    }
}
}
}
pub mod io {
pub mod input {
use std::fmt::Debug;
use std::io::Read;
use std::marker::PhantomData;
use std::path::Path;
use std::str::FromStr;

pub struct Input {
    input: Box<dyn Read>,
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
}

macro_rules! read_integer_fun {
    ($t:ident) => {
        #[allow(unused)]
        pub fn $t(&mut self) -> $t {
            self.read_integer()
        }
    };
}

impl Input {
    const DEFAULT_BUF_SIZE: usize = 4096;

    ///
    /// Using with stdin:
    /// ```no_run
    /// use algo_lib::io::input::Input;
    /// let stdin = std::io::stdin();
    /// let input = Input::new(Box::new(stdin));
    /// ```
    ///
    /// For read files use ``new_file`` instead.
    ///
    ///
    pub fn new(input: Box<dyn Read>) -> Self {
        Self {
            input,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_stdin() -> Self {
        let stdin = std::io::stdin();
        Self::new(Box::new(stdin))
    }

    pub fn new_file<P: AsRef<Path>>(path: P) -> Self {
        let file = std::fs::File::open(&path)
            .unwrap_or_else(|_| panic!("Can't open file: {:?}", path.as_ref().as_os_str()));
        Self::new(Box::new(file))
    }

    pub fn new_with_size(input: Box<dyn Read>, buf_size: usize) -> Self {
        Self {
            input,
            buf: vec![0; buf_size],
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_file_with_size<P: AsRef<Path>>(path: P, buf_size: usize) -> Self {
        let file = std::fs::File::open(&path)
            .unwrap_or_else(|_| panic!("Can't open file: {:?}", path.as_ref().as_os_str()));
        Self::new_with_size(Box::new(file), buf_size)
    }

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

    pub fn peek(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            Some(self.buf[self.at])
        } else {
            None
        }
    }

    pub fn skip_whitespace(&mut self) {
        while let Some(b) = self.peek() {
            if !char::from(b).is_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 char::from(c).is_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()
    }

    pub fn has_more_elements(&mut self) -> bool {
        !self.is_exhausted()
    }

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

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

    pub fn string_vec(&mut self, size: usize) -> Vec<Vec<u8>> {
        let mut res = Vec::with_capacity(size);
        for _ in 0usize..size {
            res.push(self.string());
        }
        res
    }

    pub fn read_line(&mut self) -> String {
        let mut res = String::new();
        while let Some(c) = self.get() {
            if c == b'\n' {
                break;
            }
            if c == b'\r' {
                if self.peek() == Some(b'\n') {
                    self.get();
                }
                break;
            }
            res.push(c.into());
        }
        res
    }

    #[allow(clippy::should_implement_trait)]
    pub fn into_iter<T: Readable>(self) -> InputIterator<T> {
        InputIterator {
            input: self,
            phantom: Default::default(),
        }
    }

    fn read_integer<T: FromStr + Debug>(&mut self) -> T
    where
        <T as FromStr>::Err: Debug,
    {
        let res = self.read_string();
        res.parse::<T>().unwrap()
    }

    fn read_string(&mut self) -> String {
        match self.next_token() {
            None => {
                panic!("Input exhausted");
            }
            Some(res) => unsafe { String::from_utf8_unchecked(res) },
        }
    }

    pub fn string_as_string(&mut self) -> String {
        self.read_string()
    }

    pub fn string(&mut self) -> Vec<u8> {
        self.read_string().into_bytes()
    }

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

    fn read_float(&mut self) -> f64 {
        self.read_string().parse().unwrap()
    }

    pub fn f64(&mut self) -> f64 {
        self.read_float()
    }

    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
        }
    }

    read_integer_fun!(i32);
    read_integer_fun!(i64);
    read_integer_fun!(i128);
    read_integer_fun!(u32);
    read_integer_fun!(u64);
    read_integer_fun!(usize);
}

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

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

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

impl Readable for f64 {
    fn read(input: &mut Input) -> Self {
        input.read_string().parse().unwrap()
    }
}

impl Readable for f32 {
    fn read(input: &mut Input) -> Self {
        input.read_string().parse().unwrap()
    }
}

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

pub struct InputIterator<T: Readable> {
    input: Input,
    phantom: PhantomData<T>,
}

impl<T: Readable> Iterator for InputIterator<T> {
    type Item = T;

    fn next(&mut self) -> Option<Self::Item> {
        self.input.skip_whitespace();
        self.input.peek().map(|_| self.input.read())
    }
}

macro_rules! read_integer {
    ($t:ident) => {
        impl Readable for $t {
            fn read(input: &mut Input) -> Self {
                input.read_integer()
            }
        }
    };
}

read_integer!(i8);
read_integer!(i16);
read_integer!(i32);
read_integer!(i64);
read_integer!(i128);
read_integer!(isize);
read_integer!(u8);
read_integer!(u16);
read_integer!(u32);
read_integer!(u64);
read_integer!(u128);
read_integer!(usize);
}
pub mod output {
use std::io::Write;

pub struct Output {
    output: Box<dyn Write>,
    buf: Vec<u8>,
    at: usize,
    auto_flush: bool,
}

impl Output {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(output: Box<dyn Write>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            auto_flush: false,
        }
    }

    pub fn new_stdout() -> Self {
        let stdout = std::io::stdout();
        Self::new(Box::new(stdout))
    }

    pub fn new_file(path: impl AsRef<std::path::Path>) -> Self {
        let file = std::fs::File::create(path).unwrap();
        Self::new(Box::new(file))
    }

    pub fn new_with_auto_flush(output: Box<dyn Write>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            auto_flush: true,
        }
    }

    pub fn flush(&mut self) {
        if self.at != 0 {
            self.output.write_all(&self.buf[..self.at]).unwrap();
            self.at = 0;
            self.output.flush().expect("Couldn't flush output");
        }
    }

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

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

    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]) {
        for i in arg {
            i.write(self);
            self.put(b'\n');
        }
    }

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

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

impl<T: Writable> Writable for Vec<T> {
    fn write(&self, output: &mut Output) {
        self[..].write(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!(u8);
write_to_string!(u16);
write_to_string!(u32);
write_to_string!(u64);
write_to_string!(u128);
write_to_string!(usize);
write_to_string!(i8);
write_to_string!(i16);
write_to_string!(i32);
write_to_string!(i64);
write_to_string!(i128);
write_to_string!(isize);
write_to_string!(f32);
write_to_string!(f64);

impl<T: Writable, U: Writable> Writable for (T, U) {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
        output.put(b' ');
        self.1.write(output);
    }
}

impl<T: Writable, U: Writable, V: Writable> Writable for (T, U, V) {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
        output.put(b' ');
        self.1.write(output);
        output.put(b' ');
        self.2.write(output);
    }
}
}
}
pub mod math {
pub mod modulo {
use crate::algo_lib::collections::last_exn::LastExn;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::input::Readable;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::io::output::Writable;
use crate::algo_lib::misc::num_traits::ConvSimple;
use crate::algo_lib::misc::num_traits::HasConstants;
use crate::algo_lib::misc::num_traits::Number;
use std::io::Write;
use std::marker::PhantomData;

pub trait Value: Clone + Copy + Eq + Default + Ord {
    fn val() -> i32;
}

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
pub struct ModWithValue<M>(i32, PhantomData<M>)
where
    M: Value;

impl<M> ModWithValue<M>
where
    M: Value,
{
    #[allow(unused)]
    pub const ZERO: Self = Self(0, PhantomData);

    #[allow(unused)]
    pub const ONE: Self = Self(1, PhantomData);

    #[allow(unused)]
    pub const TWO: Self = Self(2, PhantomData);

    fn rev_rec(a: i32, m: i32) -> i32 {
        if a == 1 {
            return a;
        }
        ((1 - Self::rev_rec(m % a, a) as i64 * m as i64) / a as i64 + m as i64) as i32
    }

    #[allow(dead_code)]
    pub fn inv(self) -> Self {
        ModWithValue(Self::rev_rec(self.0, M::val()), PhantomData)
    }

    pub fn value(&self) -> i32 {
        self.0
    }

    pub fn i64(&self) -> i64 {
        self.0 as i64
    }

    #[allow(dead_code)]
    pub fn new<T: Number>(x: T) -> Self {
        let mut x = x.to_i32();
        if x < 0 {
            x += M::val();
            if x < 0 {
                x %= M::val();
                x += M::val();
            }
        } else if x >= M::val() {
            x -= M::val();
            if x >= M::val() {
                x %= M::val();
            }
        }
        assert!(0 <= x && x < M::val());
        Self(x, PhantomData)
    }

    pub fn pown(self, pw: usize) -> Self {
        if pw == 0 {
            Self::ONE
        } else if pw == 1 {
            self
        } else {
            let half = self.pown(pw / 2);
            let res = half * half;
            if pw % 2 == 0 {
                res
            } else {
                res * self
            }
        }
    }

    pub fn gen_powers(base: Self, n: usize) -> Vec<Self> {
        let mut res = Vec::with_capacity(n);
        res.push(Self::ONE);
        for _ in 1..n {
            res.push(*res.last_exn() * base);
        }
        res
    }
}

impl<M> std::fmt::Display for ModWithValue<M>
where
    M: Value,
{
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<M> std::fmt::Debug for ModWithValue<M>
where
    M: Value + Copy + Eq,
{
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        const MAX: i32 = 100;

        if self.0 <= MAX {
            write!(f, "{}", self.0)
        } else if self.0 >= M::val() - MAX {
            write!(f, "-{}", M::val() - self.0)
        } else {
            for denom in 1..MAX {
                let num = *self * Self(denom, PhantomData);
                if num.0 <= MAX {
                    return write!(f, "{}/{}", num.0, denom);
                } else if num.0 >= M::val() - MAX {
                    return write!(f, "-{}/{}", M::val() - num.0, denom);
                }
            }
            write!(f, "(?? {} ??)", self.0)
        }
    }
}

impl<M> std::ops::Add for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    fn add(self, rhs: Self) -> Self::Output {
        let res = self.0 + rhs.0;
        if res >= M::val() {
            ModWithValue(res - M::val(), PhantomData)
        } else {
            ModWithValue(res, PhantomData)
        }
    }
}

impl<M> std::ops::AddAssign for ModWithValue<M>
where
    M: Value,
{
    fn add_assign(&mut self, rhs: Self) {
        self.0 += rhs.0;
        if self.0 >= M::val() {
            self.0 -= M::val();
        }
    }
}

impl<M> std::ops::Sub for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    fn sub(self, rhs: Self) -> Self::Output {
        let res = self.0 - rhs.0;
        if res < 0 {
            ModWithValue(res + M::val(), PhantomData)
        } else {
            ModWithValue(res, PhantomData)
        }
    }
}

impl<M> std::ops::SubAssign for ModWithValue<M>
where
    M: Value,
{
    fn sub_assign(&mut self, rhs: Self) {
        self.0 -= rhs.0;
        if self.0 < 0 {
            self.0 += M::val();
        }
    }
}

impl<M> std::ops::Mul for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    fn mul(self, rhs: Self) -> Self::Output {
        let res = (self.0 as i64) * (rhs.0 as i64) % (M::val() as i64);
        ModWithValue(res as i32, PhantomData)
    }
}

impl<M> std::ops::MulAssign for ModWithValue<M>
where
    M: Value,
{
    fn mul_assign(&mut self, rhs: Self) {
        self.0 = ((self.0 as i64) * (rhs.0 as i64) % (M::val() as i64)) as i32;
    }
}

impl<M> std::ops::Div for ModWithValue<M>
where
    M: Value,
{
    type Output = Self;

    #[allow(clippy::suspicious_arithmetic_impl)]
    fn div(self, rhs: Self) -> Self::Output {
        let rhs_inv = rhs.inv();
        self * rhs_inv
    }
}

impl<M> std::ops::DivAssign for ModWithValue<M>
where
    M: Value,
{
    #[allow(clippy::suspicious_op_assign_impl)]
    fn div_assign(&mut self, rhs: Self) {
        *self *= rhs.inv();
    }
}

impl<M> Writable for ModWithValue<M>
where
    M: Value,
{
    fn write(&self, output: &mut Output) {
        output.write_fmt(format_args!("{}", self.0)).unwrap();
    }
}

impl<M> Readable for ModWithValue<M>
where
    M: Value,
{
    fn read(input: &mut Input) -> Self {
        let i32 = input.i32();
        Self::new(i32)
    }
}

impl<M> HasConstants<ModWithValue<M>> for ModWithValue<M>
where
    M: Value,
{
    // This doesn't make much sense, but hope we never use
    const MAX: ModWithValue<M> = ModWithValue::ZERO;
    const MIN: ModWithValue<M> = ModWithValue::ZERO;
    const ZERO: ModWithValue<M> = ModWithValue::ZERO;
    const ONE: ModWithValue<M> = ModWithValue::ONE;
    const TWO: ModWithValue<M> = ModWithValue::TWO;
}

impl<M> ConvSimple<ModWithValue<M>> for ModWithValue<M>
where
    M: Value,
{
    fn from_i32(val: i32) -> ModWithValue<M> {
        ModWithValue::new(val)
    }

    fn to_i32(self) -> i32 {
        self.0
    }

    fn to_f64(self) -> f64 {
        self.0 as f64
    }
}

pub trait ConstValue: Value + Copy {
    const VAL: i32;
}

impl<V: ConstValue> Value for V {
    fn val() -> i32 {
        Self::VAL
    }
}

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
pub struct Value7();
impl ConstValue for Value7 {
    const VAL: i32 = 1_000_000_007;
}
pub type Mod7 = ModWithValue<Value7>;

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
pub struct Value9();
impl ConstValue for Value9 {
    const VAL: i32 = 1_000_000_009;
}
pub type Mod9 = ModWithValue<Value9>;

#[derive(Copy, Clone, Eq, PartialEq, Default, Ord, PartialOrd, Hash)]
#[allow(non_camel_case_types)]
pub struct Value_998_244_353();
impl ConstValue for Value_998_244_353 {
    const VAL: i32 = 998_244_353;
}
#[allow(non_camel_case_types)]
pub type Mod_998_244_353 = ModWithValue<Value_998_244_353>;

pub trait ModuloTrait: Number {
    fn mod_value() -> i32;
    fn pown(self, n: usize) -> Self;
}

impl<V: Value> ModuloTrait for ModWithValue<V> {
    fn mod_value() -> i32 {
        V::val()
    }

    fn pown(self, n: usize) -> Self {
        self.pown(n)
    }
}
}
}
pub mod misc {
pub mod binary_search {
use crate::algo_lib::misc::num_traits::Number;
use std::ops::Range;

pub fn binary_search_first_true<T>(range: Range<T>, mut f: impl FnMut(T) -> bool) -> T
where
    T: Number,
{
    // we can't store [range.start - 1] into [left], because it could overflow
    let mut left_plus_one = range.start;
    let mut right = range.end;
    while right > left_plus_one {
        let mid = left_plus_one + (right - left_plus_one) / T::TWO;
        if f(mid) {
            right = mid;
        } else {
            left_plus_one = mid + T::ONE;
        }
    }
    right
}

pub fn binary_search_last_true<T>(range: Range<T>, mut f: impl FnMut(T) -> bool) -> Option<T>
where
    T: Number,
{
    let first_false = binary_search_first_true(range.clone(), |x| !f(x));
    if first_false == range.start {
        None
    } else {
        Some(first_false - T::ONE)
    }
}

#[test]
fn simple_stress() {
    const N: usize = 50;
    for n in 1..N {
        for cnt_false in 0..=n {
            let mut a = vec![false; cnt_false];
            a.resize(n, true);
            let mut max_f_calls = ((n + 1) as f64).log2().ceil() as i32;
            let f_is_true = |id: usize| -> bool {
                max_f_calls -= 1;
                assert!(max_f_calls >= 0);
                a[id]
            };
            let result = binary_search_first_true(0..n, f_is_true);
            assert_eq!(result, cnt_false);
        }
    }
}
}
pub mod dbg_macro {
#[macro_export]
#[allow(unused_macros)]
macro_rules! dbg {
    ($first_val:expr, $($val:expr),+ $(,)?) => {
        eprint!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val);
        ($(eprint!(", {} = {:?}", stringify!($val), &$val)),+,);
        eprintln!();
    };
    ($first_val:expr) => {
        eprintln!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val)
    };
}
}
pub mod num_traits {
use std::cmp::Ordering;
use std::fmt::Debug;
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::Sub;
use std::ops::SubAssign;

pub trait HasConstants<T> {
    const MAX: T;
    const MIN: T;
    const ZERO: T;
    const ONE: T;
    const TWO: T;
}

pub trait ConvSimple<T> {
    fn from_i32(val: i32) -> T;
    fn to_i32(self) -> i32;
    fn to_f64(self) -> f64;
}

pub trait Signum {
    fn signum(&self) -> i32;
}

pub trait Number:
    Copy
    + Add<Output = Self>
    + AddAssign
    + Sub<Output = Self>
    + SubAssign
    + Mul<Output = Self>
    + MulAssign
    + Div<Output = Self>
    + DivAssign
    + PartialOrd
    + PartialEq
    + HasConstants<Self>
    + Default
    + Debug
    + Sized
    + ConvSimple<Self>
{
}

impl<
        T: Copy
            + Add<Output = Self>
            + AddAssign
            + Sub<Output = Self>
            + SubAssign
            + Mul<Output = Self>
            + MulAssign
            + Div<Output = Self>
            + DivAssign
            + PartialOrd
            + PartialEq
            + HasConstants<Self>
            + Default
            + Debug
            + Sized
            + ConvSimple<Self>,
    > Number for T
{
}

macro_rules! has_constants_impl {
    ($t: ident) => {
        impl HasConstants<$t> for $t {
            // TODO: remove `std` for new rust version..
            const MAX: $t = std::$t::MAX;
            const MIN: $t = std::$t::MIN;
            const ZERO: $t = 0;
            const ONE: $t = 1;
            const TWO: $t = 2;
        }

        impl ConvSimple<$t> for $t {
            fn from_i32(val: i32) -> $t {
                val as $t
            }

            fn to_i32(self) -> i32 {
                self as i32
            }

            fn to_f64(self) -> f64 {
                self as f64
            }
        }
    };
}

has_constants_impl!(i32);
has_constants_impl!(i64);
has_constants_impl!(i128);
has_constants_impl!(u32);
has_constants_impl!(u64);
has_constants_impl!(u128);
has_constants_impl!(usize);
has_constants_impl!(u8);

impl ConvSimple<Self> for f64 {
    fn from_i32(val: i32) -> Self {
        val as f64
    }

    fn to_i32(self) -> i32 {
        self as i32
    }

    fn to_f64(self) -> f64 {
        self
    }
}

impl HasConstants<Self> for f64 {
    const MAX: Self = Self::MAX;
    const MIN: Self = -Self::MAX;
    const ZERO: Self = 0.0;
    const ONE: Self = 1.0;
    const TWO: Self = 2.0;
}

impl<T: Number + Ord> Signum for T {
    fn signum(&self) -> i32 {
        match self.cmp(&T::ZERO) {
            Ordering::Greater => 1,
            Ordering::Less => -1,
            Ordering::Equal => 0,
        }
    }
}
}
}
pub mod seg_trees {
pub mod lazy_seg_tree {
use std::ops::Range;

use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;

///
/// Segment Tree
///
#[allow(unused)]
#[derive(Clone)]
pub struct SegTree<T: SegTreeNode> {
    n: usize,
    tree: Vec<T>,
    updates_to_push: Vec<Option<T::Update>>,
    context: T::Context,
    right_nodes: Vec<usize>,
}

#[allow(unused)]
impl<T: SegTreeNode> SegTree<T> {
    fn pull(&mut self, v: usize, vr: usize) {
        self.tree[v] = T::join_nodes(&self.tree[v + 1], &self.tree[vr], &self.context);
    }

    fn build(&mut self, v: usize, l: usize, r: usize, init_val: &T) {
        if l + 1 == r {
            self.tree[v] = init_val.clone();
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.build(v + 1, l, m, init_val);
            self.build(vr, m, r, init_val);
            self.pull(v, vr);
        }
    }

    fn push(&mut self, v: usize, l: usize, r: usize) {
        let update = self.updates_to_push[v].clone();
        self.updates_to_push[v] = None;
        match update {
            None => {}
            Some(update) => {
                let m = (l + r) >> 1;
                self.apply_update(v + 1, &update, m - l == 1);
                self.apply_update(v + ((r - l) & !1), &update, r - m == 1);
            }
        }
    }

    fn get_(&mut self, v: usize, l: usize, r: usize, ql: usize, qr: usize) -> T {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            return self.tree[v].clone();
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        let res = if ql >= m {
            self.get_(vr, m, r, ql, qr)
        } else if qr <= m {
            self.get_(v + 1, l, m, ql, qr)
        } else {
            T::join_nodes(
                &self.get_(v + 1, l, m, ql, qr),
                &self.get_(vr, m, r, ql, qr),
                &self.context,
            )
        };
        self.pull(v, vr);
        res
    }

    fn visit_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        ql: usize,
        qr: usize,
        f: &mut impl FnMut(&T),
    ) {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            f(&self.tree[v]);
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        if ql >= m {
            self.visit_(vr, m, r, ql, qr, f);
        } else if qr <= m {
            self.visit_(v + 1, l, m, ql, qr, f)
        } else {
            self.visit_(v + 1, l, m, ql, qr, f);
            self.visit_(vr, m, r, ql, qr, f);
        };
        self.pull(v, vr);
    }

    fn join_updates(current: &mut Option<T::Update>, add: &T::Update) {
        match current {
            None => *current = Some(add.clone()),
            Some(current) => T::join_updates(current, add),
        };
    }

    fn apply_update(&mut self, v: usize, update: &T::Update, is_leaf: bool) {
        T::apply_update(&mut self.tree[v], update);
        if !is_leaf {
            Self::join_updates(&mut self.updates_to_push[v], update);
        }
    }

    fn modify_(&mut self, v: usize, l: usize, r: usize, ql: usize, qr: usize, update: &T::Update) {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            self.apply_update(v, update, r - l == 1);
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        if ql >= m {
            self.modify_(vr, m, r, ql, qr, update);
        } else if qr <= m {
            self.modify_(v + 1, l, m, ql, qr, update);
        } else {
            self.modify_(v + 1, l, m, ql, qr, update);
            self.modify_(vr, m, r, ql, qr, update);
        };
        self.pull(v, vr);
    }

    pub fn update(&mut self, range: Range<usize>, update: T::Update) {
        if range.is_empty() {
            return;
        }
        assert!(!range.is_empty());
        self.modify_(0, 0, self.n, range.start, range.end, &update);
    }

    pub fn update_point(&mut self, pos: usize, new_node: T) {
        let mut l = 0;
        let mut r = self.n;
        let mut v: usize = 0;
        let mut to_pull = vec![];
        while r - l > 1 {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.push(v, l, r);
            to_pull.push((v, vr));
            if pos < m {
                r = m;
                v = v + 1;
            } else {
                l = m;
                v = vr;
            }
        }
        self.tree[v] = new_node;
        for (v, vr) in to_pull.into_iter().rev() {
            self.pull(v, vr);
        }
    }

    fn find_last_true_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        range: Range<usize>,
        f: &impl Fn(&T) -> bool,
    ) -> Option<usize> {
        if range.start >= r || l >= range.end {
            return None;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        if range.start <= l && r <= range.end {
            if !f(&self.tree[v]) {
                return None;
            }
            if r - l == 1 {
                return Some(l);
            }
        }
        self.push(v, l, r);
        if let Some(res) = self.find_last_true_(vr, m, r, range.clone(), f) {
            Some(res)
        } else {
            self.find_last_true_(v + 1, l, m, range, f)
        }
    }

    // returns position
    pub fn find_last_true(&mut self, range: Range<usize>, f: impl Fn(&T) -> bool) -> Option<usize> {
        self.find_last_true_(0, 0, self.n, range, &f)
    }

    pub fn get(&mut self, range: Range<usize>) -> T {
        if range.is_empty() {
            return T::default();
        }
        self.get_(0, 0, self.n, range.start, range.end)
    }

    pub fn visit(&mut self, range: Range<usize>, f: &mut impl FnMut(&T)) {
        if range.is_empty() {
            return;
        }
        self.visit_(0, 0, self.n, range.start, range.end, f);
    }

    pub fn new_with_context(n: usize, f: impl Fn(usize) -> T, context: T::Context) -> Self {
        assert!(n > 0);
        let tree = vec![T::default(); 2 * n - 1];
        let updates_to_push = vec![None; 2 * n - 1];
        let mut res = SegTree {
            n,
            tree,
            updates_to_push,
            context,
            right_nodes: vec![],
        };
        res.build_f(0, 0, n, &f);
        res
    }

    pub fn new(n: usize, f: impl Fn(usize) -> T) -> Self
    where
        T::Context: Default,
    {
        assert!(n > 0);
        let tree = vec![T::default(); 2 * n - 1];
        let updates_to_push = vec![None; 2 * n - 1];
        let mut res = SegTree {
            n,
            tree,
            updates_to_push,
            context: T::Context::default(),
            right_nodes: vec![],
        };
        res.build_f(0, 0, n, &f);
        res
    }

    fn build_f(&mut self, v: usize, l: usize, r: usize, f: &impl Fn(usize) -> T) {
        if l + 1 == r {
            self.tree[v] = f(l);
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.build_f(v + 1, l, m, f);
            self.build_f(vr, m, r, f);
            self.pull(v, vr);
        }
    }

    pub fn len(&self) -> usize {
        self.n
    }

    pub fn expert_get_node(&self, node: usize) -> &T {
        &self.tree[node]
    }

    pub fn expert_get_left_node(&self, node: usize) -> usize {
        node + 1
    }

    fn build_right_nodes(&mut self, v: usize, l: usize, r: usize) {
        if l + 1 == r {
            self.right_nodes.push(0);
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.right_nodes.push(vr);
            self.build_right_nodes(v + 1, l, m);
            self.build_right_nodes(vr, m, r);
        }
    }

    // TODO: shouldn't be mut
    pub fn expert_get_right_node(&mut self, node: usize) -> usize {
        if self.right_nodes.is_empty() {
            self.build_right_nodes(0, 0, self.n);
        }
        self.right_nodes[node]
    }

    // Used for Kinetic Seg Tree
    pub fn expert_rebuild_nodes(&mut self, should_rebuild: impl Fn(&T, &T::Context) -> bool) {
        self.expert_rebuild_nodes_(0, 0, self.n, &should_rebuild);
    }

    fn expert_rebuild_nodes_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        should_rebuild: &impl Fn(&T, &T::Context) -> bool,
    ) {
        if r - l <= 1 || !should_rebuild(&self.tree[v], &self.context) {
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);

        self.expert_rebuild_nodes_(v + 1, l, m, should_rebuild);
        self.expert_rebuild_nodes_(vr, m, r, should_rebuild);

        self.pull(v, vr);
    }

    pub fn update_context(&mut self, f: impl Fn(&mut T::Context)) {
        f(&mut self.context);
    }

    pub fn get_context(&self) -> &T::Context {
        &self.context
    }
}
}
pub mod seg_tree_trait {
pub trait SegTreeNode: Clone + Default {
    fn join_nodes(l: &Self, r: &Self, context: &Self::Context) -> Self;

    fn apply_update(node: &mut Self, update: &Self::Update);
    fn join_updates(current: &mut Self::Update, add: &Self::Update);

    type Update: Clone;
    type Context;
}
}
}
}
fn main() {
    let input = algo_lib::io::input::Input::new_stdin();
    let mut output = algo_lib::io::output::Output::new_stdout();
    crate::solution::run(input, output);
}