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
# 作れる数の最大は50 * 50 = 2500
# dp[i][j] = i枚使ってjを作れる場合の数

import sys
readline = sys.stdin.readline

N,A = map(int,readline().split())
X = list(map(int,readline().split()))

dp = [[0] * 2501 for i in range(N + 1)]
dp[0][0] = 1

for x in X:
  for i in range(len(dp) - 2, -1, -1):
    for j in range(len(dp[i]) - 1, -1, -1):
      if dp[i][j] == 0:
        continue
      dp[i + 1][j + x] += dp[i][j]
      
ans = 0
for i in range(1, len(dp)):
  for j in range(len(dp[i])):
    if j == i * A:
      ans += dp[i][j]
      
print(ans)