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: Wrong Answer)

package main

import (
	"fmt"
	"sort"
)

var n int
var a float64
var arr []int
var dp [51][51][2501]int

func main() {
	fmt.Scan(&n, &a)
	arr = make([]int, n)
	for i := 0; i < n; i++ {
		var j int
		fmt.Scan(&j)
		arr[i] = j
	}
	sort.Ints(arr)
	if arr[len(arr)-1] < int(a) {
		fmt.Println(0)
		return
	}
	for i := 0; i < 51; i++ {
		for j := 0; j < 51; j++ {
			for k := 0; k < 2051; k++ {
				dp[i][j][k] = -1
			}
		}
	}
	fmt.Println(rec(0, 0, 0))
}

func rec(i, j, k int) int {
	if dp[i][j][k] >= 0 {
		return dp[i][j][k]
	}
	if i == n {
		if float64(k)/float64(j) == a {
			dp[i][j][k] = 1
			return 1
		} else {
			dp[i][j][k] = 0
			return 0
		}
	}

	ret := rec(i+1, j, k) + rec(i+1, j+1, k+arr[i])
	dp[i][j][k] = ret
	return ret
}