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
from copy import deepcopy

N, A = map(int, input().split())
X = list(map(int, input().split()))

for i in range(N):
    X[i] -= A

cnt = [0] * 5000

for x in X:
    cnt2 = [0] * 5000
    for i in range(-2500, 2500):
        cnt2[i + x] += cnt[i]
    cnt2[x] += 1
    for i in range(5000):
        cnt2[i] += cnt[i]
    cnt = deepcopy(cnt2)

print(cnt[0])
