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

public class Main {
    static class FastScanner {
        private final java.io.InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if (ptr < buflen) return true;
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (java.io.IOException e) {
                e.printStackTrace();
            }
            return buflen > 0;
        }
        private byte readByte() {
            return hasNextByte() ? buffer[ptr++ ] : -1;
        }
        private static boolean isPrintableChar(byte c) {
            return 32 < c || c < 0;
        }
        private static boolean isNumber(int c) {
            return '0' <= c && c <= '9';
        }
        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++ ;
            return hasNextByte();
        }
        public String next() {
            if (!hasNext()) throw new java.util.NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            byte b;
            while (isPrintableChar(b = readByte())) sb.appendCodePoint(b);
            return sb.toString();
        }
        public final long nextLong() {
            if (!hasNext()) throw new java.util.NoSuchElementException();
            long n = 0;
            try {
                byte b = readByte();
                if (b == '-') {
                    while(isNumber(b = readByte())) n = n * 10 + '0' - b;
                    return n;
                } else if (!isNumber(b)) throw new NumberFormatException();
                do n = n * 10 + b - '0'; while (isNumber(b = readByte()));
            } catch (java.util.NoSuchElementException e) {
            }
            return n;
        }
        public final int nextInt() {
            if (!hasNext()) throw new java.util.NoSuchElementException();
            int n = 0;
            try {
                byte b = readByte();
                if (b == '-') {
                    while(isNumber(b = readByte())) n = n * 10 + '0' - b;
                    return n;
                } else if (!isNumber(b)) throw new NumberFormatException();
                do n = n * 10 + b - '0'; while (isNumber(b = readByte()));
            } catch (java.util.NoSuchElementException e) {
            }
            return n;
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    static class BIT {
        int []A;
        BIT(int size) {
            A =  new int[size + 1];
        }

        void add(int x, int v) {
            for (long i = x + 1; i < A.length; i+= i & (-i)) {
                A[(int)i] += v;
            }
        }

        int get(int x) {
            int s = 0;
            for (int i = x + 1; i > 0; i-= i & (-i)) {
                s += A[i];
            }
            return s;
        }

        int search(int global, int sum) {
            int x = 0;
            int s = 0;
            for (int b = 1 << 20; b > 0; b = (b >> 1)) {
                if (x + b < A.length && s + A[x + b] <= global - sum) {
                    x += b;
                    s += A[x];
                }
            }
            return x;
        }

    }


    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        int n = scanner.nextInt();
        BIT bit = new BIT(n);
        int q = scanner.nextInt();
        int []N = new int[n];
        List<Integer> []QueryMap = new List[n + 1];
        for (int i = 0; i < n; i++) {
            N[i] = (i + 1) - scanner.nextInt();
            QueryMap[i] = new LinkedList<>();
        }
        int [][]Q = new int[q][3];
        for (int i = 0; i < q; i++) {
            Q[i][0] = scanner.nextInt();
            Q[i][1] = n - scanner.nextInt() - 1;
            Q[i][2] = 0;
            QueryMap[Q[i][1]].add(i);
        }
        int ss = 0;
        int lo, hi, m, v;
        for (int i = 0; i < n; i++) {
            if (N[i] == 0) {
                bit.add(i + 1, 1);
                //System.out.println(i);
            } else if (N[i] >= 0 && ss >= N[i]) {
               bit.add(bit.search(ss, N[i]) , 1);
            }
            if (ss >= N[i] && N[i] >= 0) ss++;
            for (Integer queryIndex : QueryMap[i]) {
                Q[queryIndex][2] = ss - bit.get(Q[queryIndex][0]);
            }
        }
        PrintWriter out = new PrintWriter(System.out);
        for (int i = 0; i < q; i++) {
            out.println(Q[i][2]);
        }
        out.flush();
    }
}