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(arg: Array<String>) {
    val (N, K) = listOfInt()
    val X = listOfInt()
    val dp = Array(N + 1) { Array(N + 1) { LongArray(N * 50 + 1) } }
    dp[0][0][0] = 1
    for (i in 0 until N) {
        for (j in 0 until N) {
            for (k in 0 until N * 50 + 1) {
                if (dp[i][j][k] == 0L) continue
                dp[i + 1][j + 1][k + X[i]] += dp[i][j][k]
                dp[i + 1][j][k] += dp[i][j][k]
            }
        }
    }
    var ans = 0L
    for (j in 1 .. N) ans += dp[N][j][K * j]
    println(ans)

}

fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfLong() = listOfString().map(String::toLong)
fun listOfInt(delta: Int = 0) = listOfString().map { Integer.parseInt(it) + delta }