Problem 1024. -- Max Sum Plus Plus

## HDU_1024: Max Sum Plus Plus

Time Limit: 1000 MS  Memory Limit: 32 MB   64bit IO Format: %I64d
Submitted: 11  Accepted: 7
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## Description

Now I think you have got an AC in Ignatius.L's "Max Sum" problem. To be a brave ACMer, we always challenge ourselves to more difficult problems. Now you are faced with a more difficult problem.

Given a consecutive number sequence S1, S2, S3, S4 ... Sx, ... Sn (1 ≤ x ≤ n ≤ 1,000,000, -32768 ≤ Sx ≤ 32767). We define a function sum(i, j) = Si + ... + Sj (1 ≤ i ≤ j ≤ n).

Now given an integer m (m > 0), your task is to find m pairs of i and j which make sum(i1, j1) + sum(i2, j2) + sum(i3, j3) + ... + sum(im, jm) maximal (ix ≤ iy ≤ jx or ix ≤ jy ≤ jx is not allowed).

But Im lazy, I don't want to write a special-judge module, so you don't have to output m pairs of i and j, just output the maximal summation of sum(ix, jx)(1 ≤ x ≤ m) instead. ^_^

## Input

Each test case will begin with two integers m and n, followed by n integers S1, S2, S3 ... Sn.
Process to the end of file.

## Output

Output the maximal summation described above in one line.

## Sample Input 1 3 1 2 3
2 6 -1 4 -2 3 -2 3

## Sample Output

6
8

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## HINT

Huge input, scanf and dynamic programming is recommended.

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