Let a_1, …, a_n be an array of n positive integers. In one operation, you can choose an index i such that a_i = i, and remove a_i from the array (after the removal, the remaining parts are concatenated).

The weight of a is defined as the maximum number of elements you can remove.

You must answer q independent queries (x, y): after replacing the x first elements of a and the y last elements of a by n+1 (making them impossible to remove), what would be the weight of a?

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 3 ⋅ 10^5) — the length of the array and the number of queries.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — elements of the array.

The i-th of the next q lines contains two integers x and y (x, y ≥ 0 and x+y < n).

Output

Print q lines, i-th line should contain a single integer — the answer to the i-th query.

Examples

Input


13 5
2 2 3 9 5 4 6 5 7 8 3 11 13
3 1
0 0
2 4
5 0
0 12


Output


5
11
6
1
0


Input


5 2
1 4 1 2 4
0 0
1 0


Output


2
0

Note

Explanation of the first query:

After making first x = 3 and last y = 1 elements impossible to remove, a becomes [×, ×, ×, 9, 5, 4, 6, 5, 7, 8, 3, 11, ×] (we represent 14 as × for clarity).

Here is a strategy that removes 5 elements (the element removed is colored in red):

  * [×, ×, ×, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, ×] 
  * [×, ×, ×, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, ×] 
  * [×, ×, ×, 9, 4, \color{red}{6}, 5, 7, 8, 3, ×] 
  * [×, ×, ×, 9, 4, 5, 7, \color{red}{8}, 3, ×] 
  * [×, ×, ×, 9, 4, 5, \color{red}{7}, 3, ×] 
  * [×, ×, ×, 9, 4, 5, 3, ×] (final state) 



It is impossible to remove more than 5 elements, hence the weight is 5.
#include <bits/stdc++.h>
#pragma GCC optimize("O3,no-stack-protector")
#pragma GCC target( \
    "sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
using namespace std;
struct SegTree {
  vector<int> t;
  vector<int> changed;
  SegTree(int len) : t(4 * len, 0), changed(4 * len, 0) {}
  void Push(int v, int vl, int vr) {
    if (changed[v] == 0) {
      return;
    }
    t[v] += changed[v];
    if (vl != vr) {
      changed[2 * v] += changed[v];
      changed[2 * v + 1] += changed[v];
    }
    changed[v] = 0;
  }
  int Get(int pos) { return GetImpl(pos, 1, 0, t.size() / 4 - 1); }
  int GetImpl(int pos, int v, int vl, int vr) {
    Push(v, vl, vr);
    if (vl == vr) {
      return t[v];
    }
    int m = (vl + vr) / 2;
    if (pos > m) {
      return GetImpl(pos, 2 * v + 1, m + 1, vr);
    }
    return GetImpl(pos, 2 * v, vl, m);
  }
  void Inc(int l, int r) { IncImpl(l, r, 1, 0, t.size() / 4 - 1); }
  void IncImpl(int l, int r, int v, int vl, int vr) {
    Push(v, vl, vr);
    if (l > r) {
      return;
    }
    if (vl == l and vr == r) {
      changed[v] = 1;
      Push(v, vl, vr);
      return;
    }
    int m = (vl + vr) / 2;
    IncImpl(l, min(r, m), 2 * v, vl, m);
    IncImpl(max(l, m + 1), r, 2 * v + 1, m + 1, vr);
    t[v] = max(t[2 * v], t[2 * v + 1]);
  }
  int FirstLeq(int bound) {
    return FirstLeqImpl(bound, 1, 0, t.size() / 4 - 1);
  }
  int FirstLeqImpl(int bound, int v, int vl, int vr) {
    Push(v, vl, vr);
    if (t[v] < bound) {
      return -1;
    }
    if (vl == vr) {
      return vl;
    }
    int m = (vl + vr) / 2;
    int r = FirstLeqImpl(bound, 2 * v + 1, m + 1, vr);
    if (r == -1) {
      return FirstLeqImpl(bound, 2 * v, vl, m);
    }
    return r;
  }
};
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  int len, qc;
  cin >> len >> qc;
  vector<int> vec(len);
  for (int i = 0; i < len; ++i) {
    int x;
    cin >> x;
    vec[i] = i + 1 - x;
  }
  vector<vector<pair<int, int>>> qbuf(len);
  vector<int> ans(qc);
  for (int q = 0; q < qc; ++q) {
    int x, y;
    cin >> x >> y;
    qbuf[len - 1 - y].emplace_back(x, q);
  }
  SegTree tree(len);
  for (int r = 0; r < len; ++r) {
    if (vec[r] >= 0) {
      int leq_i = min(r, tree.FirstLeq(vec[r]));
      tree.Inc(0, leq_i);
    }
    for (auto&& [l, q] : qbuf[r]) {
      ans[q] = tree.Get(l);
    }
  }
  for (auto&& x : ans) {
    cout << x << '\n';
  }
  return 0;
}
