IntermediatePrefix Sums2000 ms256 MB

Prefix Sum Queries

Answer range sum queries on a list using 1-based inclusive indexes.

Statement

Answer range sum queries on a list using 1-based inclusive indexes.

Input

First line: `n q`. Second line: `n` integers. Next `q` lines: `l r`.

Output

Print each range sum on its own line.

Constraints

  • `1 <= n, q <= 100000`

Examples

Example 1

Input

5 3
2 4 6 8 10
1 3
2 5
4 4

Output

12
28
8

Use prefix sums to answer each range quickly.

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