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

Example Output

2
1
1
4