Problem:
Score : 300 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

Input

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

N A
x_1 x_2 ... x_N

Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Sample Input 1

4 8
7 9 8 9

Sample 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.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample 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

Sample Output 4

8589934591

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

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

//dp[i][j][k] = i枚目までのカードでj枚選んで合計がkである組合せ
//カードを選ばない　dp[i + 1][j][k] += dp[i][j][k]
//カードを選ぶ　　　dp[i + 1][j + 1][k + x[i]] += dp[i][j][k]

#include<stdio.h>
long long int dp[51][51][2510] = { { { 1 } } };
int main() {
	int N, A;
	scanf("%d%d", &N, &A);
	int *X = (int *)malloc(sizeof(int)*N);
	for (int i = 1; i <= N; i++)
	{
		scanf("%d", &X[i]);
	}

	for (int i = 1; i <= N; i++)
	{
		for (int j = 0; j <= N; j++)
		{
			for (int k = 0; k <= 2500; k++)//
			{
				if (k < X[i]) {
					dp[i][j][k] = dp[i - 1][j][k];
				}
				else if (j >= 1) {
					dp[i][j][k] = dp[i - 1][j - 1][k - X[i]] + dp[i - 1][j][k];
				}
			}
		}
	}
		long long int ans = 0;
		for (int j = 1; j <= N; j++) {
			ans += dp[N][j][j*A];
		}
		printf("%lld\n", ans);
		return 0;
	}