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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

class SegmentTreeRMQ {
  public int M, H, N;
  public int[] st;

  public SegmentTreeRMQ(int n) {
    N = n;
    M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
    H = M >>> 1;
    st = new int[M];
    Arrays.fill(st, 0, M, Integer.MAX_VALUE);
  }

  public SegmentTreeRMQ(int[] a) {
    N = a.length;
    M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
    H = M >>> 1;
    st = new int[M];
    for (int i = 0; i < N; i++) {
      st[H + i] = a[i];
    }
    Arrays.fill(st, H + N, M, Integer.MAX_VALUE);
    for (int i = H - 1; i >= 1; i--)
      propagate(i);
  }

  public void update(int pos, int x) {
    st[H + pos] = x;
    for (int i = (H + pos) >>> 1; i >= 1; i >>>= 1)
      propagate(i);
  }

  private void propagate(int i) {
    st[i] = Math.min(st[2 * i], st[2 * i + 1]);
  }

  public int minx(int l, int r) {
    int min = Integer.MAX_VALUE;
    if (l >= r)
      return min;
    while (l != 0) {
      int f = l & -l;
      if (l + f > r)
        break;
      int v = st[(H + l) / f];
      if (v < min)
        min = v;
      l += f;
    }

    while (l < r) {
      int f = r & -r;
      int v = st[(H + r) / f - 1];
      if (v < min)
        min = v;
      r -= f;
    }
    return min;
  }

  public int min(int l, int r) {
    return l >= r ? 0 : min(l, r, 0, H, 1);
  }

  private int min(int l, int r, int cl, int cr, int cur) {
    if (l <= cl && cr <= r) {
      return st[cur];
    } else {
      int mid = cl + cr >>> 1;
      int ret = Integer.MAX_VALUE;
      if (cl < r && l < mid) {
        ret = Math.min(ret, min(l, r, cl, mid, 2 * cur));
      }
      if (mid < r && l < cr) {
        ret = Math.min(ret, min(l, r, mid, cr, 2 * cur + 1));
      }
      return ret;
    }
  }

  public int firstle(int l, int v) {
    int cur = H + l;
    while (true) {
      if (st[cur] <= v) {
        if (cur < H) {
          cur = 2 * cur;
        } else {
          return cur - H;
        }
      } else {
        cur++;
        if ((cur & cur - 1) == 0)
          return -1;
        if ((cur & 1) == 0)
          cur >>>= 1;
      }
    }
  }

  public int lastle(int l, int v) {
    int cur = H + l;
    while (true) {
      if (st[cur] <= v) {
        if (cur < H) {
          cur = 2 * cur + 1;
        } else {
          return cur - H;
        }
      } else {
        if ((cur & cur - 1) == 0)
          return -1;
        cur--;
        if ((cur & 1) == 1)
          cur >>>= 1;
      }
    }
  }
}

@SuppressWarnings("unused")
public class Main {

  private static void solve() {
    int n = ni();
    int q = ni();
    int[] a = na(n);
    for (int i = 0; i < n; i++) {
      a[i] = -a[i];
    }
    SegmentTreeRMQ st = new SegmentTreeRMQ(a);

    for (int i = 0; i < q; i++) {
      int t = ni();
      int x = ni();
      int y = ni();
      if (t == 1) {
        st.update(x - 1, -y);
      } else if (t == 2) {
        out.println(-st.min(x - 1, y));
      } else {
        int ret = st.firstle(x - 1, -y) + 1;
        out.println(ret == 0 ? n + 1 : ret);
      }
    }
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}