Score : $400$ points

Problem Statement

You are given a sequence of non-negative integers $A=(a_1,a_2,\ldots,a_N)$.

Let $S$ be the set of non-negative integers that can be the sum of $K$ terms in $A$ (with distinct indices).

Find the greatest multiple of $D$ in $S$. If there is no multiple of $D$ in $S$, print -1 instead.

Constraints

• $1 \leq K \leq N \leq 100$
• $1 \leq D \leq 100$
• $0 \leq a_i \leq 10^9$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $K$ $D$

$a_1$ $\ldots$ $a_N$

Output

Print the answer.

4 2 2
1 2 3 4

6

Here are all the ways to choose two terms in $A$.

• Choose $a_1$ and $a_2$, whose sum is $1+2=3$.
• Choose $a_1$ and $a_3$, whose sum is $1+3=4$.
• Choose $a_1$ and $a_4$, whose sum is $1+4=5$.
• Choose $a_2$ and $a_3$, whose sum is $2+3=5$.
• Choose $a_2$ and $a_4$, whose sum is $2+4=6$.
• Choose $a_3$ and $a_4$, whose sum is $3+4=7$.

Thus, we have $S=\{3,4,5,6,7\}$. The greatest multiple of $2$ in $S$ is $6$, so you should print $6$.

3 1 2
1 3 5

-1

In this example, we have $S=\{1,3,5\}$. Nothing in $S$ is a multiple of $2$, so you should print -1.