**Time limit:**1.00 s**Memory limit:**512 MB

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