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()))

sumX = sum(xs)

# dp[i][j]: i枚で合計jとなる選び方の個数
dp = [[0] * (sumX + 1) for _ in range(N + 1)]
dp[0][0] = 1
for k, x in enumerate(xs):
    for i in reversed(range(k + 1)):
        for j in range(sumX + 1):
            if dp[i][j] == 0: continue
            dp[i + 1][j + x] += dp[i][j]

# 平均A = i枚で合計(A*i)
ans = 0
for i in range(1, min(N, sumX // A) + 1):
    ans += dp[i][A * i]
print(ans)
