# Max Sum Plus Plus

## 描述

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 S

Now given an integer m (m > 0), your task is to find m pairs of i and j which make sum(i

But I`m 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(i

Given a consecutive number sequence S

_{1}, S_{2}, S_{3}, S_{4}... S_{x}, ... S_{n}(1 ≤ x ≤ n ≤ 1,000,000, -32768 ≤ S_{x}≤ 32767). We define a function sum(i, j) = S_{i}+ ... + S_{j}(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(i

_{1}, j_{1}) + sum(i_{2}, j_{2}) + sum(i_{3}, j_{3}) + ... + sum(i_{m}, j_{m}) maximal (i_{x}≤ i_{y}≤ j_{x}or i_{x}≤ j_{y}≤ j_{x}is not allowed).But I`m 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(i

_{x}, j_{x})(1 ≤ x ≤ m) instead. ^_^## 输入

Each test case will begin with two integers m and n, followed by n integers S

Process to the end of file.

_{1}, S_{2}, S_{3}... S_{n}.Process to the end of file.

## 输出

Output the maximal summation described above in one line.

## 样例

样例输入 #1

```
1 3 1 2 3
2 6 -1 4 -2 3 -2 3
```

样例输出 #1

```
6
8
<i style="font-size:1px"> </i>
```

## 提示

Huge input, scanf and dynamic programming is recommended.