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 Go (1.6) (judge verdict: Accepted)

// ProblemURL : https://atcoder.jp/contests/abc044/tasks/arc060_a
// ---------------------------------------------
package main

import "fmt"

const inf = 1 << 60

func main() {
	var n, a int
	fmt.Scan(&n, &a)
	xs := make([]int, n+1)
	xs[0] = -inf
	for i := 1; i <= n; i++ {
		fmt.Scan(&xs[i])
	}

	dp := [51][51][2501]int{}
	dp[0][0][0] = 1
	for i := 1; i <= n; i++ {
		for j := 0; j <= n; j++ {
			for k := 0; k <= 2500; k++ {
				dp[i][j][k] += dp[i-1][j][k]
				if j-1 >= 0 && k-xs[i] >= 0 {
					dp[i][j][k] += dp[i-1][j-1][k-xs[i]]
				}
			}
		}
	}

	ans := 0
	for j := 1; j <= n; j++ {
		ans += dp[n][j][a*j]
	}
	fmt.Println(ans)
}