Missing Coin Sum Queries

You have n coins with positive integer values. The coins are numbered 1,2,\dots,n. Your task is to process q queries of the form: "if you can use coins a \dots b, what is the smallest sum you cannot produce?"

Input

The first input line has two integers n and q: the number of coins and queries. The second line has n integers x_1,x_2,\dots,x_n: the value of each coin. Finally, there are q lines that describe the queries. Each line has two values a and b: you can use coins a \dots b.

Output

Print the answer for 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

5 3
2 9 1 2 7
2 4
4 4
1 5

Output

4
1
6

Explanation: First you can use coins [9,1,2], then coins [2] and finally coins [2,9,1,2,7].