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Some crazy guy shows you a *n* x *n* grid of integers.

He then asks you to find the maximum value of the sum of all integers inside any *k* x *k* northwest oriented right angled triangle in the grid.

The *k* x *k* triangle must reside FULLY in the grid.

Being a smart programmer, you decide to use a computer to solve the madman's question.

## Input

The first line of input will consist of 2 integers *n* (1 ≤ *n* ≤ 5,000) and k (1 ≤ *k* ≤ *n*).

The following *n* lines will contain *n* integers each. Each integer *a* will satisfy 1 ≤ *a* ≤ 400.

## Output

Output the maximum sum possible as described above.## Grading

For 20% of the test cases, *n* ≤ 50.

For 50% of the cases (including the above 20%), *n* ≤ 300.

## Sample Input 1

5 3 1 2 3 1 3 3 1 1 1 4 1 2 3 1 5 5 5 5 5 5 5 5 3 5 5

## Sample Output 1

22

## Explanation for Sample Output 1

The*k*x

*k*northwest oriented right angled triangle that gives the maximum sum is this portion:

3 1 5 5 5 3

which gives 22.

Notice that the incomplete triangle bit which gives a better sum of 23:

5 5 5 3 5

is not allowed.

### Tags

### Subtasks and Limits

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

1 | 0 | 1 | 5s | 256MB | Average |

2 | 100 | 10 | 5s | 256MB | Average |

### Judge Compile Command

g++ ans.cpp -o trianglesum -Wall -static -O2 -lm -m64 -s -w -std=gnu++14 -fmax-errors=512