You are given an array of n integers and q queries. In each query, your task is to calculate the maximum subarray sum in the range [a,b].

Empty subarrays (with sum 0) are allowed.

Input

The first line contains two integers n and q: the number of elements and the number of queries.

Then there are n integers x_1,x_2,\ldots,x_n: the contents of the array.

Finally there are q lines that describe the queries. Each line has two integers a and b.

Output

Print the answer for each query.

Constraints

• 1 \le n, q\le 2 \cdot 10^5
• -10^9 \le x_i \le 10^9
• 1 \le a \le b \le n

Example

Input:

8 4
2 5 1 -2 3 -1 -7 1
2 4
2 5
6 7
4 8

Output:

6
7
0
3