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
N,A = map(int, input().split())
xs = list(map(int, input().split()))
"""
dp[i][j][n] : i枚目において、j枚選んだときの合計がnになる場合の数
dp[i+1][j+1][n+x] = dp[i][j][n] * (x) + dp[i][j+1][n+x]
dp[0][0][0] = 1
"""
Nx = 2550
dp = [[[0]*Nx for i in range(N+10)] for j in range(N+10)]
dp[0][0][0] = 1

for i in range(N):
    x = xs[i]
    for j in range(N):
        for n in range(Nx):
            dp[i+1][j][n] = dp[i][j][n]
    for j in range(N):
        for n in range(Nx):
            if n + x >= Nx:continue
            dp[i+1][j+1][n+x] = dp[i][j][n] + dp[i][j+1][n+x]
    # print(i,dp[i])
cnts = dp[N]
ans = 0
for i in range(1,N+1):
    ans += cnts[i][A*i]
print(ans)