C. Fixed Point Removaltime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet 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?InputThe 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).OutputPrint q lines, i-th line should contain a single integer  — the answer to the i-th query.ExamplesInput
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
NoteExplanation 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.
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

5 11 6 1 0 
['binary search', 'constructive algorithms', 'data structures', 'greedy', 'two pointers', '*2300']