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,queue,math,copy,itertools
from fractions import gcd
sys.setrecursionlimit(10**7)
input = sys.stdin.readline
INF = 10**18
MOD = 10**9 + 7
LI = lambda : [int(x) for x in input().split()]
N,A = LI()
_LI = lambda : [int(x)-A for x in input().split()]
X = _LI()

m = [0 for _ in range(50*N)]
Base = 25 * N

for i in range(N):
    m2 = copy.copy(m)
    for j in range(len(m)):
        if m[j]:
            if 0<= j + X[i] < len(m2):
                m2[j+X[i]] += m[j]
    m = m2
    m[X[i] + Base] += 1
print (m[Base])