COCI '20 Contest 6 #5 Index

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Points: 15 (partial)
Time limit: 2.5s
Memory limit: 512M

Problem type

The h-index is an author-level metric that measures both the productivity and citation impact of the publications of a scientist or scholar. It is defined as the maximum value of h such that the given author has published h papers that have each been cited at least h times.

Our Mirko is nearing retirement. In his life he had published n papers and now q times he asks himself the following:

I wonder, what would be my h-index had I only published papers l_i through r_i?

Help him calculate the answers.

Input Specification

The first line contains integers n and q (1 \le n, q \le 200\,000), the number of papers and the number of questions.

The second line contains n integers p_i (1 \le p_i \le 200\,000), where p_i is the number of citations of the i^\text{th} paper.

The following q lines each contain two integers l_i and r_i (1 \le l_i \le r_i \le n), the endpoints from the i^\text{th} question.

Output Specification

Output q lines. In the i^\text{th} line output the answer to the i^\text{th} question.


1201 \le n, q \le 1\,000
2401 \le n, q \le 50\,000
350No additional constraints.

Sample Input 1

7 6
3 2 3 1 1 4 7
3 4
1 7
1 6
4 5
1 2
5 7

Sample Output 1



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