Median

You are given an array ~a~ of ~n~ elements. Furthermore, there are ~q~ queries. Each query is of the form l r: What is the median element in the range ~[l,r]~. In this case, we consider the median of an even length list the minimum of the two middle values.

Input Format

The first line is n q, the number of elements and queries. The next line contains the array a. The next q lines each contain two integers l r, a query.

Sample Input

5 1
1 2 3 4 5
1 4

Sample Output

3

Constraints

~1 \le n,q \le 1e5~ ~1 \le a[i] \le 1e4~