Problem:
Score : 100 points

Problem Statement

You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

The type of i-th query is represented by T_i.

T_i=1: You are given two integers X_i,V_i. Replace the value of A_{X_i} with V_i.

T_i=2: You are given two integers L_i,R_i. Calculate the maximum value among A_{L_i},A_{L_i+1},\cdots,A_{R_i}.

T_i=3: You are given two integers X_i,V_i. Calculate the minimum j such that X_i \leq j \leq N, V_i \leq A_j. If there is no such j, answer j=N+1 instead.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq A_i \leq 10^9

1 \leq Q \leq 2 \times 10^5

1 \leq T_i \leq 3

1 \leq X_i \leq N, 0 \leq V_i \leq 10^9 (T_i=1,3)

1 \leq L_i \leq R_i \leq N (T_i=2)

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N Q
A_1 A_2 \cdots A_N
First query
Second query
\vdots
Q-th query

Each query is given in the following format:

If T_i=1,3,

T_i X_i V_i

If T_i=2,

T_i L_i R_i

Output

For each query with T_i=2, 3, print the answer.

Sample Input 1

5 5
1 2 3 2 1
2 1 5
3 2 3
1 3 1
2 2 4
3 1 3

Sample Output 1

3
3
2
6

First query: Print 3, which is the maximum of (A_1,A_2,A_3,A_4,A_5)=(1,2,3,2,1).

Second query: Since 3>A_2, j=2 does not satisfy the condition．Since 3 \leq A_3, print j=3.

Third query: Replace the value of A_3 with 1. It becomes A=(1,2,1,2,1).

Fourth query: Print 2, which is the maximum of (A_2,A_3,A_4)=(2,1,2).

Fifth query: Since there is no j that satisfies the condition, print j=N+1=6.

Solution in Rust (1.42.0) (judge verdict: Accepted)

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//https://github.com/manta1130/Competitive_Programming_Template_Rust

mod segtree {

///汎用のセグメント木
pub struct SegTreeBasic<T, F> {
    //n: usize,
    v: Vec<T>,
    init: T,
    parent_generator: F,
}

impl<T, F> SegTreeBasic<T, F>
where
    T: PartialOrd + Clone + Copy,
    F: Fn(T, T) -> T,
{
    ///セグメント木を構築する。
    ///
    /// # Examples
    /// ```ignore
    /// let mut segtree = SegTreeBasic::new(100, usize::max_value(), |a, b| std::cmp::min(a, b));
    /// //要素数100のRMQを構築する。
    /// ```
    pub fn new(n: usize, init: T, parent_generator: F) -> SegTreeBasic<T, F> {
        let mut size = 1;
        while size < n {
            size *= 2;
        }
        let v = vec![init; size * 2 - 1];
        SegTreeBasic {
            //n: size,
            v: v,
            init: init,
            parent_generator: parent_generator,
        }
    }

    ///[l,r)の要素をparent_generatorに基づいて計算する。
    pub fn get(&mut self, l: usize, r: usize) -> T {
        let vlen = self.v.len();
        self._get(l, r, 0, 0, (vlen + 1) / 2)
    }

    fn _get(&mut self, l: usize, r: usize, now: usize, a: usize, b: usize) -> T {
        if a >= r || b <= l {
            self.init
        } else if l <= a && b <= r {
            self.v[now]
        } else {
            let bufa = self._get(l, r, now * 2 + 1, a, (a + b) / 2);
            let bufb = self._get(l, r, now * 2 + 2, (a + b) / 2, b);
            let cond = &self.parent_generator;
            cond(bufa, bufb)
        }
    }

    ///任意の要素を書き換える。
    pub fn update(&mut self, index: usize, value: T) {
        let offset = (self.v.len() + 1) / 2 - 1;
        self.v[offset + index] = value;
        let mut parent = index + offset;
        loop {
            parent = (parent - 1) / 2;
            let cond = &self.parent_generator;
            self.v[parent] = cond(self.v[parent * 2 + 1], self.v[parent * 2 + 2]);
            if parent == 0 {
                break;
            }
        }
    }
}
}

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};

use segtree::*;

#[fastout]
fn main() {
    input! {
        n:usize,q:usize,
        mut a:[usize;n]
    }
    let mut s = SegTreeBasic::new(n + 1, 0, |a, b| std::cmp::max(a, b));
    for (i, x) in a.iter().enumerate() {
        s.update(i, *x);
    }
    for _ in 0..q {
        input! {
            t:usize,x:usize,y:usize
        }
        if t == 1 {
            s.update(x - 1, y);
        } else if t == 2 {
            println!("{}", s.get(x - 1, y));
        } else {
            if s.get(x - 1, n) < y {
                println!("{}", n + 1);
            } else {
                let mut ok = n as isize;
                let mut ng = x as isize - 1;
                while ok - ng > 1 {
                    let mid = (ok + ng) / 2;
                    if s.get(x - 1, mid as usize) >= y {
                        ok = mid;
                    } else {
                        ng = mid;
                    }
                }
                println!("{}", ok);
            }
        }
    }
}