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 collections

N, A = [int(s) for s in input().split()]

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

S = [collections.Counter() for _ in range(51)]

S[0][0] = 1
for i, xi in enumerate(x):
    prev = [(k,s,c) for k in range(i+1) for s,c in S[k].items()]
    for (k,s,c) in prev:
        S[k+1][s+xi] += c
    #print(sum(sum(S[k].values()) for k in range(i+1)))

ans = 0
for (k, s, c) in ((k,s,c) for k in range(1,N+1) for s,c in S[k].items()):
    if A*k == s:
        ans += c

print(ans)