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

N, A = map(int, sys.stdin.readline().strip().split())
X = list(map(int, sys.stdin.readline().strip().split()))

# iまでのカードをj枚使って、合計でkである組み合わせ数
MAX_N = N*50 + 1
dp = [[[0 for _ in range(MAX_N)] for _ in range(N+1)] for _ in range(N+1)]

dp[0][0][0] = 1
for i in range(N):
    for j in range(N):
        for k in range(MAX_N):
            if dp[i][j][k] > 0:
                # i+1番目のカードを選ばない
                dp[i+1][j][k] += dp[i][j][k]
                # i+1番目のカードを選ぶ
                dp[i+1][j+1][k+X[i]] += dp[i][j][k]

ans = 0
for i in range(1, N+1):
    ans += dp[N][i][A*i]
print(ans)