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
input = sys.stdin.readline

N, A = [int(x) for x in input().split()]
x = [int(x) - A for x in input().split()]

dp = [[0] * 5001 for _ in range(N + 1)]
dp[0][0 + 2500] = 1

for i in range(1, N + 1):
    for j in range(-2500, 2501):
        if 5000 >= j + 2500 - x[i - 1] >= 0:
            dp[i][j + 2500] = dp[i - 1][j + 2500 - x[i - 1]] + dp[i - 1][j + 2500]
        else:
            dp[i][j + 2500] = dp[i - 1][j + 2500]

print(dp[N][0 + 2500] - 1)