Tak and Cards

AtCoder

IDarc060_a

Time2000ms

Memory256MB

Difficulty—

Tak has $N$ cards. On the $i$\-th $(1 \leq i \leq N)$ card is written an integer $x_i$. He is selecting one or more cards from these $N$ cards, so that the average of the integers written on the selected cards is exactly $A$. In how many ways can he make his selection? ## Constraints * $1 \leq N \leq 50$ * $1 \leq A \leq 50$ * $1 \leq x_i \leq 50$ * $N,\,A,\,x_i$ are integers. ## Input The input is given from Standard Input in the following format: $N$ $A$ $x_1$ $x_2$ $...$ $x_N$ ## Partial Score * $200$ points will be awarded for passing the test set satisfying $1 \leq N \leq 16$. [samples]

Samples

Input #1

4 8
7 9 8 9

Output #1

5

*   The following are the $5$ ways to select cards such that the average is $8$:
    *   Select the $3$\-rd card.
    *   Select the $1$\-st and $2$\-nd cards.
    *   Select the $1$\-st and $4$\-th cards.
    *   Select the $1$\-st, $2$\-nd and $3$\-rd cards.
    *   Select the $1$\-st, $3$\-rd and $4$\-th cards.

Input #2

3 8
6 6 9

Output #2

Input #3

8 5
3 6 2 8 7 6 5 9

Output #3

Input #4

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Output #4

8589934591

*   The answer may not fit into a $32$\-bit integer.

API Response (JSON)

{
  "problem": {
    "name": "Tak and Cards",
    "description": {
      "content": "Tak has $N$ cards. On the $i$\\-th $(1 \\leq i \\leq N)$ card is written an integer $x_i$. He is selecting one or more cards from these $N$ cards, so that the average of the integers written on the selec",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc060_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Tak has $N$ cards. On the $i$\\-th $(1 \\leq i \\leq N)$ card is written an integer $x_i$. He is selecting one or more cards from these $N$ cards, so that the average of the integers written on the selec...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments