Max Multiple

AtCoder

IDabc281_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $K$ $D$ $a_1$ $\ldots$ $a_N$ [samples]

Samples

Input #1

4 2 2
1 2 3 4

Output #1

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 $6$.

Input #2

3 1 2
1 3 5

Output #2

\-1

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

API Response (JSON)

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    "name": "Max Multiple",
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      "content": "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 greate",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc281_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of non-negative integers $A=(a_1,a_2,\\ldots,a_N)$.\nLet $S$ be the set of non-negative integers that can be the sum of $K$ terms in $A$ (with distinct indices).\nFind the greate...",
      "is_translate": false,
      "language": "English"
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