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(a) for a in input().split()]
PO = [x-A for x in X if x > A]
NE = [A-x for x in X if x < A]
ZE = N - len(PO) - len(NE)

Y = [1] + [0] * 3000
Z = [1] + [0] * 3000

for i in PO:
    for j in range(2800)[::-1]:
        Y[i+j] += Y[j]
for i in NE:
    for j in range(2800)[::-1]:
        Z[i+j] += Z[j]

ans = -1
for i in range(len(Y)):
    ans += Y[i] * Z[i] * (2**ZE)
print(ans)