Static Range Minimum Queries

Given an array of n integers, your task is to process q queries of the form: what is the minimum value in range [a,b]?

Input

The first input line has two integers n and q: the number of values and queries. The second line has n integers x_1,x_2,\dots,x_n: the array values. Finally, there are q lines describing the queries. Each line has two integers a and b: what is the minimum value in range [a,b]?

Output

Print the result of each query.

Constraints

$1 \le n,q \le 2 \cdot 10^5$

$1 \le x_i \le 10^9$

$1 \le a \le b \le n$

Example

Input

8 4
3 2 4 5 1 1 5 3
2 4
5 6
1 8
3 3

Output

2
1
1
4