Static Range Minimum Queries

• 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