Zero Remainder Sum

题意翻译

给定$n*m$的矩阵$A$，和一个整数$k$，要求每行只能选取不超过一半的元素，且总的选择元素的和要是k的倍数，求最大值。

题目描述

You are given a matrix $ a $ of size $ n \times m $ consisting of integers. You can choose no more than $ \left\lfloor\frac{m}{2}\right\rfloor $ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by $ k $ and this sum is the maximum. In other words, you can choose no more than a half (rounded down) of elements in each row, you have to find the maximum sum of these elements divisible by $ k $ . Note that you can choose zero elements (and the sum of such set is $ 0 $ ).

输入输出格式

输入格式

The first line of the input contains three integers $ n $ , $ m $ and $ k $ ( $ 1 \le n, m, k \le 70 $ ) — the number of rows in the matrix, the number of columns in the matrix and the value of $ k $ . The next $ n $ lines contain $ m $ elements each, where the $ j $ -th element of the $ i $ -th row is $ a_{i, j} $ ( $ 1 \le a_{i, j} \le 70 $ ).

输出格式

Print one integer — the maximum sum divisible by $ k $ you can obtain.

输入输出样例

输入样例 #1

3 4 3
1 2 3 4
5 2 2 2
7 1 1 4

输出样例 #1

24

输入样例 #2

5 5 4
1 2 4 2 1
3 5 1 2 4
1 5 7 1 2
3 8 7 1 2
8 4 7 1 6

输出样例 #2

56

说明

In the first example, the optimal answer is $ 2 $ and $ 4 $ in the first row, $ 5 $ and $ 2 $ in the second row and $ 7 $ and $ 4 $ in the third row. The total sum is $ 2 + 4 + 5 + 2 + 7 + 4 = 24 $ .

题意翻译

给定$n*m$的矩阵$A$，和一个整数$k$，要求每行只能选取不超过一半的元素，且总的选择元素的和要是k的倍数，求最大值。