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.
import java.util.*;
import java.io.*;

public class C1404 {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int q = sc.nextInt();
		int[] a = sc.nextIntArr(n);
		ArrayList<int[]>[] query = new ArrayList[n + 1];
		for (int i = 0; i < query.length; i++) {
			query[i] = new ArrayList<int[]>();
		}
		int[] ans = new int[q];
		for (int i = 0; i < q; i++) {
			int u = sc.nextInt();
			int v = sc.nextInt();
			query[n - v].add(new int[] { i, u + 1 });
		}
		int[] need = new int[n + 1];
		for (int i = 1; i < need.length; i++) {
			need[i] = (i) - a[i];
		}
//		pw.println(Arrays.toString(need));
		int[] p = new int[n + 1];
		FenwickTree ft = new FenwickTree(n);
		for (int i = 1; i <= n; i++) {
			if (need[i] < 0) {
				p[i] = -1;
			} else if (need[i] == 0) {
				p[i] = i;
				ft.point_inc(i);
			} else {
				int par = ft.findIndex(need[i]);
				if (par == -1) {
					p[i] = -1;
				} else {
					p[i] = par;
					ft.point_inc(par);
				}
			}
			for (int[] qu : query[i]) {
				ans[qu[0]] = ft.rsq(qu[1], i);
			}
//			pw.println(ft);
		}
		for (int x : ans) {
			pw.println(x);
		}
		pw.close();

	}

	static class MergeTree {

	}

	static class FenwickTree { // one-based DS

		int n;
		int[] ft;
		int total;

		FenwickTree(int size) {
			n = size;
			ft = new int[n + 1];
		}

		public String toString() {
			String s = "";
			for (int i = 1; i <= n; i++) {
				s += rsq(i, i) + " ";
			}
			return s;
		}

		int rsq(int b) // O(log n)
		{
			int sum = 0;
			while (b > 0) {
				sum += ft[b];
				b -= b & -b;
			}
			return sum;
		}

		int rsq(int a, int b) {
			return rsq(b) - rsq(a - 1);
		}

		void point_inc(int k) // O(log n), update = increment
		{
			total++;
			while (k <= n) {
				ft[k]++;
				k += k & -k;
			} // min?
		}

		int findIndex(int cumFreq) {
			cumFreq = total - cumFreq;
			if (cumFreq < 0) {
				return -1;
			}
			int msk = n;
			while ((msk & (msk - 1)) != 0)
				msk ^= msk & -msk; // msk will contain the MSB of n

			int idx = 0;
			while (msk != 0) {
				int tIdx = idx + msk;
				if (tIdx <= n && cumFreq >= ft[tIdx]) {
					idx = tIdx;
					cumFreq -= ft[tIdx];
				}
				msk >>= 1;
			}

			return idx + 1;
		}
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n + 1];
			for (int i = 1; i <= n; i++) {
				arr[i] = Integer.parseInt(next());
			}
			return arr;
		}

	}

}
