Let $a_1, \ldots, a_n$ 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 $q$ ($1 \le n, q \le 3 \cdot 10^5$)  — the length of the array and the number of queries.

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

The $i$-th of the next $q$ lines contains two integers $x$ and $y$ ($x, y \ge 0$ 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 $[\times, \times, \times, 9, 5, 4, 6, 5, 7, 8, 3, 11, \times]$ (we represent $14$ as $\times$ for clarity).

Here is a strategy that removes $5$ elements (the element removed is colored in red):  $[\times, \times, \times, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, \times]$  $[\times, \times, \times, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, \times]$  $[\times, \times, \times, 9, 4, \color{red}{6}, 5, 7, 8, 3, \times]$  $[\times, \times, \times, 9, 4, 5, 7, \color{red}{8}, 3, \times]$  $[\times, \times, \times, 9, 4, 5, \color{red}{7}, 3, \times]$  $[\times, \times, \times, 9, 4, 5, 3, \times]$ (final state) 

It is impossible to remove more than $5$ elements, hence the weight is $5$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from sys import stdin\n\ndef bitadd(a,w,bit):\n \n    x = a\n    while x <= (len(bit)-1):\n        bit[x] += w\n        x += x & (-1 * x)\n \ndef bitsum(a,bit):\n \n    ret = 0\n    x = a\n    while x > 0:\n        ret += bit[x]\n        x -= x & (-1 * x)\n    return ret\n\nclass RangeBIT:\n\n    def __init__(self,N,indexed):\n        self.bit1 = [0] * (N+2)\n        self.bit2 = [0] * (N+2)\n        self.mode = indexed\n\n    def bitadd(self,a,w,bit):\n \n        x = a\n        while x <= (len(bit)-1):\n            bit[x] += w\n            x += x & (-1 * x)\n \n    def bitsum(self,a,bit):\n \n        ret = 0\n        x = a\n        while x > 0:\n            ret += bit[x]\n            x -= x & (-1 * x)\n        return ret\n    \n    def add(self,l,r,w):\n\n        l = l + (1-self.mode)\n        r = r + (1-self.mode)\n        self.bitadd(l,-1*w*l,self.bit1)\n        self.bitadd(r,w*r,self.bit1)\n        self.bitadd(l,w,self.bit2)\n        self.bitadd(r,-1*w,self.bit2)\n\n    def sum(self,l,r):\n        l = l + (1-self.mode)\n        r = r + (1-self.mode)\n        ret =  self.bitsum(r,self.bit1) + r * self.bitsum(r,self.bit2)\n        ret -= self.bitsum(l,self.bit1) + l * self.bitsum(l,self.bit2)\n\n        return ret\n\nn,q = list(map(int,stdin.readline().split()))\na = list(map(int,stdin.readline().split()))\n\nqs = [ [] for i in range(n+1) ]\nans = [None] * q\n\nfor loop in range(q):\n    x,y = list(map(int,stdin.readline().split()))\n    l = x+1\n    r = n-y\n    qs[r].append((l,loop))\n\nBIT = [0] * (n+1)\n\nfor r in range(1,n+1):\n\n    b = r-a[r-1]\n\n    if b >= 0:\n\n        L = 1\n        R = r+1\n        while R-L != 1:\n            M = (L+R)//2\n\n            if bitsum(M,BIT) >= b:\n                L = M\n            else:\n                R = M\n\n        if bitsum(L,BIT) >= b:\n            bitadd(1,1,BIT)\n            bitadd(L+1,-1,BIT)\n\n\n    for ql,qind in qs[r]:\n        ans[qind] = bitsum(ql,BIT)\n\nfor i in ans:\n    print (i)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17389