1433F · Zero Remainder Sum

Problem: 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 $0$).

Input Format: 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 $a_{i, j}$ ($1 \le a_{i, j} \le 70$).

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

Note: 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 $2 + 4 + 5 + 2 + 7 + 4 = 24$.