Problem: 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.

Example

Input

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


Output

3
3
2
6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int MAX_N=262144;
vector<int64_t> seg(MAX_N*2-1);
int64_t qu(int a,int b,int k,int l, int r){
  if(r<=a||b<=l){
    return -1;
  }
  else if(a<=l&&r<=b){
    return seg[k];
  }
  else{
    int64_t X=qu(a,b,k*2+1,l,(l+r)/2);
    int64_t Y=qu(a,b,k*2+2,(l+r)/2,r);
    return max(X,Y);
  }
}

void chmax(int64_t a,int b){
  int D=MAX_N-1+b;
  seg[D]=a;
  while(D>0){
    D--;
    D/=2;
    seg[D]=max(seg[2*D+1],seg[2*D+2]);
  }
}

int main() {
  int N,Q;
  cin>>N>>Q;
  for(int i=1;i<=N;i++){
    int64_t a;
    cin>>a;
    chmax(a,i);
  }
  for(int i=0;i<Q;i++){
    int64_t a,b,c;
    cin>>a>>b>>c;
    if(a==1){
      chmax(c,b);
    }
    else if(a==2){
      cout<<qu(b,c+1,0,0,MAX_N)<<endl;
    }
    else{
      if(qu(b,N+1,0,0,MAX_N)<c){
        cout<<N+1<<endl;
      }
      else{
        int l=b,r=N+1;
        while(r-l>1){
          int D=(l+r)/2;
          if(qu(b,D,0,0,MAX_N)>=c){
            r=D;
          }
          else{
            l=D;
          }
        }
        cout<<l<<endl;
      }
    }
  }
}