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 = list(map(int, input().split(' ')))
# ans_map[x][y] x+1枚選んで和がyになる組み合わせの数
ans_map = [[0 for i in range(50*(j+1)+1)] for j in range(N)]
count = 0
for n in X:
    count += 1
    for x in range(0, count)[::-1]:
        for y in range(len(ans_map[x])):
            if ans_map[x][y] != 0:
                ans_map[x+1][y+n] += ans_map[x][y]
    ans_map[0][n] += 1
ans = 0
for i in range(N):
    ans += ans_map[i][A*(i+1)]
print(ans)
