Subarray Sum Queries II

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