Fixed Point Removal

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.

inputFormat

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).

outputFormat

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.

样例

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

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