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Static Range Sum Queries

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Time limit 4000/4000/4000/5000 ms. Memory limit 65000/65000/65000/65000 Kb. Difficulty Alpha


Given an array of n integers, your task is to process q queries of the form: what is the sum of values 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 x1,x2,…,xn: the array values.

Finally, there are q lines describing the queries. Each line has two integers a and b: what is the sum of values in range [a,b]?

Output

Print the result of each query.

Constraints
1≤n,q≤2⋅105
1≤xi≤109
1≤a≤b≤n

Example
Input:
8 4
3 2 4 5 1 1 5 3
2 4
5 6
1 8
3 3

Output:
11
2
24
4


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