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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (n, a) = readLine()!!.split(" ").map(String::toInt)
    var dp = Array(n+1, {Array(a*n+1, {0.toLong()})}) 
    var dp_copy = Array(n+1, {Array(a*n+1, {0.toLong()})}) 
    val x = readLine()!!.split(" ").map(String::toInt)
    dp[0][0] = 1.toLong()
    dp_copy[0][0] = 1.toLong()
    for(i in 1..n){
        for(j in 0..n-1){
            for(k in 0..n*a-x[i-1]){
                dp_copy[j+1][k+x[i-1]] += dp[j][k]
            }
        }
        for(j in 0..n){
            for(k in 0..n*a){
                dp[j][k] = dp_copy[j][k]
            }
        }
    }
    var ans = 0.toLong()
    for(i in 1..n) ans += dp[i][i*a]
    println(ans)
}