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.
from sys import stdin
def bitadd(a,w,bit):
    x = a
    while x <= (len(bit)-1):bit[x] += w;x += x & (-1 * x)
def bitsum(a,bit):
    ret = 0;x = a
    while x > 0:ret += bit[x];x -= x & (-1 * x)
    return ret
class RangeBIT:
    def __init__(self,N,indexed):self.bit1 = [0] * (N+2);self.bit2 = [0] * (N+2);self.mode = indexed
    def bitadd(self,a,w,bit): 
        x = a
        while x <= (len(bit)-1):bit[x] += w;x += x & (-1 * x) 
    def bitsum(self,a,bit): 
        ret = 0;x = a
        while x > 0:ret += bit[x];x -= x & (-1 * x)
        return ret    
    def add(self,l,r,w):l = l + (1-self.mode);r = r + (1-self.mode);self.bitadd(l,-1*w*l,self.bit1);self.bitadd(r,w*r,self.bit1);self.bitadd(l,w,self.bit2);self.bitadd(r,-1*w,self.bit2)
    def sum(self,l,r):l = l + (1-self.mode);r = r + (1-self.mode);ret =  self.bitsum(r,self.bit1) + r * self.bitsum(r,self.bit2);ret -= self.bitsum(l,self.bit1) + l * self.bitsum(l,self.bit2);return ret
n,q = map(int,stdin.readline().split());a = list(map(int,stdin.readline().split()));qs = [ [] for i in range(n+1) ];ans = [None] * q;BIT = [0] * (n+1)
for loop in range(q):x,y = map(int,stdin.readline().split());l = x+1;r = n-y;qs[r].append((l,loop))
for r in range(1,n+1):
    b = r-a[r-1]
    if b >= 0:
        L = 1;R = r+1
        while R-L != 1:
            M = (L+R)//2
            if bitsum(M,BIT) >= b:L = M
            else:R = M
        if bitsum(L,BIT) >= b:bitadd(1,1,BIT);bitadd(L+1,-1,BIT)
    for ql,qind in qs[r]:ans[qind] = bitsum(ql,BIT)
for i in ans:print (i) 