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## Problem Description

Damian has an array *A* of *N* numbers, and wants to find the minimum contiguous sum that can be formed.

However, he decides that this is too trivial. Thus, he decides to swap up to *K* pairs of numbers first, in the hope of making the sum even smaller.

What is the new minimum sum possible?

## Input

The first line contains two integers, *N* and *K*, the number of integers and the maximum number of swaps possible.

The second line contains *N* space-separated integers, representing the numbers of the array.

## Output

The output should contain one line containing one integer, the minimum contiguous sum that can be formed.

## Limits

For all subtasks, |*A _{i}*| ≤ 10

^{6}; 1 ≤

*N*≤ 100.

Subtask 1 (19%): *K* = 0.

Subtask 2 (27%): *K* = 1.

Subtask 3 (54%): 0 ≤ *K* ≤ 100.

Subtask 4 (0%): Sample Testcases.

## Sample Testcase 1

### Input

8 1 -1 5 -5 -3 2 -5 -4 0

### Output

-18

## Sample Testcase 1 Explanation

Damian swaps the number at position 0 with the number at position 4.

The minimum contiguous sum can then be formed in this way: 2 5 (-5 -3 -1 -5 -4 0)

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 19 | 10 | 1s | 256MB | Minimum |

2 | 27 | 10 | 1s | 256MB | Minimum |

3 | 54 | 31 | 1s | 256MB | Minimum |

4 | 0 | 1 | 1s | 256MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o minimumswap -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512