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


Output

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

Examples

Input

4 8
7 9 8 9


Output

5


Input

3 8
6 6 9


Output

0


Input

8 5
3 6 2 8 7 6 5 9


Output

19


Input

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

8589934591
import sys

rl = sys.stdin.readline


def solve():
    N, A = map(int, rl().split())
    x = list(map(int, rl().split()))
    
    y = [xi - A for xi in x]
    dp = [[0] * 5001 for _ in range(N + 1)]
    dp[0][2500] = 1
    
    for i in range(N):
        for j in range(5001):
            if 0 <= j - y[i] < 5001:
                dp[i + 1][j] = dp[i][j] + dp[i][j - y[i]]
            else:
                dp[i + 1][j] = dp[i][j]
    print(dp[N][2500] - 1)


if __name__ == '__main__':
    solve()
