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
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline

n,a,*x = map(int,read().split())

x = [i-a for i in x]

d = {0:1}
for i in x:
    nd = d.copy()
    for k,v in d.items():
        if k+i in nd:
            nd[k+i] += v
        else:
            nd[k+i] = v

    d = nd

    #print(d)
print(d[0]-1)