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())
x = [int(x)-a for x in input().split()]

ans = [[0]*5001 for _ in range(n)]  # -2500 ~ 2500

for i in range(n):
    if i == 0:
        ans[0][x[i]+2500] += 1
    else:
        for j in range(5001):
            if 5000 >= j-x[i] >= 0:
                ans[i][j] = ans[i-1][j] + ans[i-1][j-x[i]]
        ans[i][x[i]+2500] += 1

print(ans[n-1][2500])