Problem:
Score : 300 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

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.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

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

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.

Solution in Python (3.4.3) (judge verdict: Accepted)

import numpy as np
import bisect
import itertools

#N, K = map(int, input().split())
#A = list(map(int,input().split()))
#A = [int(input()) for _ in range(N)]
#LR = [list(map(int, input().split())) for _ in range(D)]

N, A = map(int, input().split())
X = [int(i)-A for i in input().split()]

SIZE = N*50
## dp[i][SIZE+j]: i番目までの数字を使って、平均がjになる組み合わせの総数
## 初期化
dp = [[0 for i in range(2*SIZE+1)] for j in range(N+1)]
for i in range(2*SIZE+1): dp[0][i] = 0
dp[0][SIZE] = 1 ## dp[N][SIZE]が答え
  
## DP
for i in range(N):
  for j in range(2*SIZE+1):
    if j-X[i]<0 or j-X[i]>2*SIZE:
      dp[i+1][j] = dp[i][j]
    else:
      dp[i+1][j] = dp[i][j] + dp[i][j-X[i]]

print(dp[N][SIZE]-1)