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

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].