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
def solve():
	N,A = map(int,raw_input().split())
	x = map(int,raw_input().split())
	ofs = N*50; M = ofs*2 + 1
	DP = [[0]*M for i in xrange(N+1)]
	DP[0][ofs] = 1
	for i in xrange(N):
		for j in xrange(M):
			if DP[i][j] == 0: continue
			DP[i+1][j+x[i]-A] += DP[i][j]
			DP[i+1][j] += DP[i][j]
	print DP[N][ofs] - 1
solve()