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
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, A = mapint()
Xs = list(mapint())
Xs.sort()
dp = [[[0]*2501 for _ in range(N+1)] for _ in range(N+1)]
dp[0][0][0] = 1

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

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