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)

package main

import "fmt"

const (
	MAX_N = 50
	MAX_A = 50
)

func main() {
	var N, A int
	var x [MAX_N + 1]int

	var dp [MAX_N + 1][MAX_N + 1][MAX_N*MAX_A + 1]int64

	fmt.Scanf("%d %d", &N, &A)
	for i := 0; i < N; i++ {
		fmt.Scanf("%d", &x[i+1])
	}

	for i := 0; i < N; i++ {
		dp[i][0][0] = 1
	}

	for i := 1; i <= N; i++ {
		for j := 1; j <= i; j++ {
			for k := 1; k <= A*N; k++ {
				if k < x[i] {
					dp[i][j][k] = dp[i-1][j][k]
				} else {
					dp[i][j][k] = dp[i-1][j][k] + dp[i-1][j-1][k-x[i]]
				}
			}
		}
	}

	ans := int64(0)
	for j := 1; j <= N; j++ {
		ans += dp[N][j][j*A]
	}

	fmt.Printf("%d\n", ans)
}