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>
using namespace std;
using ll = long long;
const int MAXN = 300005;
const int INF = 987654321;
int N, Q;
int arr[MAXN];
struct SegmentTree {
  int vals[MAXN * 4 + 1], delta[MAXN * 4 + 1];
  SegmentTree() {
    for (int i = 0; i < MAXN; i++) {
      vals[i] = 0;
      delta[i] = 0;
    }
  }
  void propagate(int n) {
    delta[n * 2] += delta[n];
    delta[n * 2 + 1] += delta[n];
    vals[n * 2] += delta[n];
    vals[n * 2 + 1] += delta[n];
    delta[n] = 0;
  }
  void update(int l, int r, int v, int n = 1, int lb = 0, int ub = MAXN - 1) {
    if (lb > r || ub < l)
      return;
    else if (lb >= l && ub <= r) {
      delta[n] += v;
      vals[n] += v;
      return;
    }
    propagate(n);
    update(l, r, v, n * 2, lb, (lb + ub) / 2);
    update(l, r, v, n * 2 + 1, (lb + ub) / 2 + 1, ub);
    vals[n] = max(vals[n * 2], vals[n * 2 + 1]);
  }
  int query(int l, int r, int n = 1, int lb = 0, int ub = MAXN - 1) {
    if (lb > r || ub < l)
      return 0;
    else if (lb >= l && ub <= r)
      return vals[n];
    propagate(n);
    return max(query(l, r, n * 2, lb, (lb + ub) / 2),
               query(l, r, n * 2 + 1, (lb + ub) / 2 + 1, ub));
  }
  int queryLowerBound(int r, int v, int n = 1, int lb = 0, int ub = MAXN - 1) {
    if (lb > r || vals[n] < v)
      return -INF;
    else if (lb == ub)
      return lb;
    propagate(n);
    if ((lb + ub) / 2 + 1 <= r && vals[n * 2 + 1] >= v)
      return queryLowerBound(r, v, n * 2 + 1, (lb + ub) / 2 + 1, ub);
    else
      return queryLowerBound(r, v, n * 2, lb, (lb + ub) / 2);
  }
};
SegmentTree weights;
struct Query {
  int x, y, i;
};
Query queries[MAXN];
int answers[MAXN];
void solve() {
  cin >> N >> Q;
  for (int i = 0; i < N; i++) cin >> arr[i];
  int x, y;
  for (int i = 0; i < Q; i++) {
    cin >> x >> y;
    y = N - 1 - y;
    queries[i] = {x, y, i};
  }
  sort(queries, queries + Q,
       [](const Query& a, const Query& b) { return a.y < b.y; });
  int queryI = 0;
  for (int i = 0; i < N; i++) {
    int weightNeeded = i - (arr[i] - 1);
    if (weightNeeded >= 0) {
      int largestBoundary = min(i, weights.queryLowerBound(i, weightNeeded));
      if (largestBoundary != -INF) {
        weights.update(0, largestBoundary, 1);
      }
    }
    for (; queryI < Q && queries[queryI].y == i; queryI++) {
      answers[queries[queryI].i] =
          weights.query(queries[queryI].x, queries[queryI].x);
    }
  }
  for (int i = 0; i < Q; i++) {
    cout << answers[i] << '\n';
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int T = 1;
  for (int i = 0; i < T; i++) solve();
  return 0;
}
