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.

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

```
$N$ $K$ $D$
$a_1$ $\ldots$ $a_N$
```

Print the answer.

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

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.

-1

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