COCI '13 Contest 5 #4 Domine

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Points: 12 (partial)
Time limit: 1.0s
Memory limit: 64M

Problem type

Mirko has a chessboard with N rows and just three columns. Slavica has written an integer on each field. Mirko has K dominoes at his disposal, their dimensions being 2 \times 1, and has to arrange all of them on the board without overlapping, in a way that each domino covers exactly two fields of the board. He can rotate the dominoes as he pleases.

Help Mirko cover the largest sum of numbers possible with the dominoes!

Input Specification

The first line of input contains the integer N (1 \le N \le 1\,000), the number of rows, and K (1 \le K \le 1\,000), the number of dominoes available.

Each of the following N lines contains three integers written in the i^\text{th} row of the board. All numbers will be less than 10^6 by absolute value.

Output Specification

The first and only line of output must contain the maximal sum possible to cover with exactly K dominoes.

Sample Input 1

5 3
2 1 -1
1 3 2
0 2 3
2 1 1
3 3 0

Sample Output 1


Explanation for Sample Output 1

It is optimal to place all dominoes horizontally and along the right edge of the second row, right edge of the third row and along the left edge of the final row.

Sample Input 2

2 2
0 4 1
3 5 1

Sample Output 2



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