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 sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n,a = list(map(int, input().split()))
x = list(map(lambda x: int(x)-a, input().split()))
size = max(1, sum(abs(item) for item in x))
# 0: 
dp = [[0]*(2*size+1) for _ in range(n+1)]
dp[0][size+1] = 1
for i in range(1,n+1):
    xx = x[i-1]
    for j in range(2*size+1):
        dp[i][j] = dp[i-1][j]
        if 0<=j-xx<2*size+1:
            dp[i][j] += dp[i-1][j-xx]
print(dp[n][size+1]-1)