// https://contest.ucup.ac/contest/1893/problem/9727
use crate::algo_lib::collections::segment_tree::{SegmentTree, SegmentTreeNode};
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::test_type::TaskType;
use crate::algo_lib::misc::test_type::TestType;
use crate::algo_lib::numbers::num_traits::bit_ops::BitOps;
type PreCalc = ();
fn solve(input: &mut Input, out: &mut Output, _test_case: usize, _data: &mut PreCalc) {
    let n = input.read_size();
    let q = input.read_size();
    let a = input.read_long_vec(n);
    #[derive(Copy, Clone)]
    enum State {
        None,
        One(usize),
        More,
    }
    #[derive(Clone)]
    struct Node {
        and: i64,
        state: Vec<State>,
        delta: i64,
        single: State,
    }
    impl Node {
        fn single(a: i64, i: usize) -> Self {
            let mut state = Vec::with_capacity(63);
            for j in 0..63 {
                if a.is_set(j) {
                    state.push(State::None);
                } else {
                    state.push(State::One(i));
                }
            }
            Node {
                and: a,
                state,
                delta: i64::MAX,
                single: State::One(i),
            }
        }
    }
    impl SegmentTreeNode for Node {
        fn new(_left: usize, _right: usize) -> Self {
            Self {
                and: i64::MAX,
                state: vec![State::None; 63],
                delta: i64::MAX,
                single: State::More,
            }
        }
        fn join(&mut self, left_val: &Self, right_val: &Self) {
            self.and = left_val.and & right_val.and;
            for i in 0..63 {
                self.state[i] = match (left_val.state[i], right_val.state[i]) {
                    (State::None, x) | (x, State::None) => x,
                    _ => State::More,
                };
            }
        }
        fn accumulate(&mut self, value: &Self) {
            self.and &= value.delta;
            for i in 0..63 {
                if !value.delta.is_set(i) {
                    self.state[i] = self.single;
                }
            }
            self.delta &= value.delta;
        }
        fn reset_delta(&mut self) {
            self.delta = i64::MAX;
        }
    }
    let mut st = SegmentTree::gen(n, |i| Node::single(a[i], i));
    for _ in 0..q {
        let command = input.read_int();
        match command {
            1 => {
                let l = input.read_size() - 1;
                let r = input.read_size();
                let x = input.read_long();
                st.update(
                    l..r,
                    &Node {
                        delta: x,
                        and: 0,
                        state: Vec::new(),
                        single: State::More,
                    },
                );
            }
            2 => {
                let s = input.read_size() - 1;
                let x = input.read_long();
                st.point_update(s, Node::single(x, s));
            }
            3 => {
                let l = input.read_size() - 1;
                let r = input.read_size();
                let node = st.query(l..r);
                let mut pos = None;
                for i in (0..63).rev() {
                    if let State::One(x) = node.state[i] {
                        pos = Some(x);
                        break;
                    }
                }
                let ans = if let Some(pos) = pos {
                    st.query(l..pos).and & st.query(pos + 1..r).and
                } else {
                    node.and
                };
                out.print_line(ans);
            }
            _ => unreachable!(),
        }
    }
}
pub static TEST_TYPE: TestType = TestType::Single;
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,
    }
}


fn main() {
    let mut sin = std::io::stdin();
    let input = crate::algo_lib::io::input::Input::new(&mut sin);
    let mut stdout = std::io::stdout();
    let output = crate::algo_lib::io::output::Output::new(&mut stdout);
    run(input, output);
}
pub mod algo_lib {
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 segment_tree {
use crate::algo_lib::collections::bounds::clamp;
use crate::algo_lib::misc::direction::Direction;
use crate::when;
use std::marker::PhantomData;
use std::ops::RangeBounds;
#[allow(unused_variables)]
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 },
        }
    }
}
#[derive(Clone)]
pub struct SegmentTree<Node> {
    n: usize,
    nodes: Vec<Node>,
}
impl<Node: SegmentTreeNode> SegmentTree<Node> {
    pub fn new(n: usize) -> Self {
        Self::gen(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::gen(n, |_| iter.next().unwrap())
    }
    pub fn gen<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 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,
    eol: bool,
}
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,
            eol: true,
        }
    }
    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,
            eol: true,
        }
    }
    pub fn get(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            self.at += 1;
            if res == b'\r' {
                self.eol = true;
                if self.refill_buffer() && self.buf[self.at] == b'\n' {
                    self.at += 1;
                }
                return Some(b'\n');
            }
            self.eol = res == 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) }
    }
    pub fn is_exhausted(&mut self) -> bool {
        self.peek().is_none()
    }
    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 fn is_eol(&self) -> bool {
        self.eol
    }
}
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
}
}
pub mod output {
use crate::algo_lib::collections::vec_ext::default::default_vec;
use std::cmp::Reverse;
use std::io::{stderr, Stderr, 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>,
    separator: u8,
}
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,
            separator: b' ',
        }
    }
    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,
            separator: b' ',
        }
    }
    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(self.separator);
            }
            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
    }
    pub fn separator(&self) -> u8 {
        self.separator
    }
    pub fn set_separator(&mut self, separator: u8) {
        self.separator = separator;
    }
}
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); $(out.put(out
        .separator); self.$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, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, RemAssign, Sub, 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 bit_ops {
use crate::algo_lib::numbers::num_traits::algebra::{One, Zero};
use std::ops::{
    BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Not, RangeInclusive,
    Shl, Sub,
};
use std::ops::{ShlAssign, Shr, ShrAssign};
pub trait BitOps: Copy + BitAnd<
        Output = Self,
    > + BitAndAssign + BitOr<
        Output = Self,
    > + BitOrAssign + BitXor<
        Output = Self,
    > + BitXorAssign + Not<
        Output = Self,
    > + Shl<
        usize,
        Output = Self,
    > + ShlAssign<
        usize,
    > + Shr<usize, Output = Self> + ShrAssign<usize> + Zero + One + PartialEq {
    #[inline]
    fn bit(at: usize) -> Self {
        Self::one() << at
    }
    #[inline]
    fn is_set(&self, at: usize) -> bool {
        (*self >> at & Self::one()) == Self::one()
    }
    #[inline]
    fn set_bit(&mut self, at: usize) {
        *self |= Self::bit(at);
    }
    #[inline]
    fn unset_bit(&mut self, at: usize) {
        *self &= !Self::bit(at);
    }
    #[must_use]
    #[inline]
    fn with_bit(mut self, at: usize) -> Self {
        self.set_bit(at);
        self
    }
    #[must_use]
    #[inline]
    fn without_bit(mut self, at: usize) -> Self {
        self.unset_bit(at);
        self
    }
    #[inline]
    fn flip_bit(&mut self, at: usize) {
        *self ^= Self::bit(at);
    }
    #[must_use]
    #[inline]
    fn flipped_bit(mut self, at: usize) -> Self {
        self.flip_bit(at);
        self
    }
    fn all_bits(n: usize) -> Self {
        let mut res = Self::zero();
        for i in 0..n {
            res.set_bit(i);
        }
        res
    }
    fn iter_all(n: usize) -> RangeInclusive<Self> {
        Self::zero()..=Self::all_bits(n)
    }
}
pub struct BitIter<T> {
    cur: T,
    all: T,
    ended: bool,
}
impl<T: Copy> BitIter<T> {
    pub fn new(all: T) -> Self {
        Self {
            cur: all,
            all,
            ended: false,
        }
    }
}
impl<T: BitOps + Sub<Output = T>> Iterator for BitIter<T> {
    type Item = T;
    fn next(&mut self) -> Option<Self::Item> {
        if self.ended {
            return None;
        }
        let res = self.cur;
        if self.cur == T::zero() {
            self.ended = true;
        } else {
            self.cur = (self.cur - T::one()) & self.all;
        }
        Some(res)
    }
}
impl<
    T: Copy + BitAnd<Output = Self> + BitAndAssign + BitOr<Output = Self> + BitOrAssign
        + BitXor<Output = Self> + BitXorAssign + Not<Output = Self>
        + Shl<usize, Output = Self> + ShlAssign<usize> + Shr<usize, Output = Self>
        + ShrAssign<usize> + One + Zero + PartialEq,
> BitOps for T {}
pub trait Bits: BitOps {
    fn bits() -> u32;
}
macro_rules! bits_integer_impl {
    ($($t:ident $bits:expr),+) => {
        $(impl Bits for $t { fn bits() -> u32 { $bits } })+
    };
}
bits_integer_impl!(
    i128 128, i64 64, i32 32, i16 16, i8 8, isize 64, u128 128, u64 64, u32 32, u16 16,
    u8 8, usize 64
);
}
pub mod invertible {
pub trait Invertible {
    type Output;
    fn inv(&self) -> Option<Self::Output>;
}
}
}
}
}