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)

import java.math.*

fun main(args: Array<String>) {
    val (N, A) = readInputLine().split(" ").map { it.toInt() }
    val xs = readInputLine().split(" ").map { it.toInt() - A }
    
    val dp = Array(N + 1, { LongArray(50 * N) })
    
    dp[0][(A - 1) * N] = 1L
    
    for ((i, x) in xs.withIndex()) {
        for (j in 0 until 50 * N) {
            dp[i + 1][j] = dp[i][j]
        }
        for (j in Math.max(0, -x) until Math.min(50 * N, 50 * N - x)) {
            dp[i + 1][j + x] += dp[i][j]
        }
    }
    
    println(dp[N][(A - 1) * N] - 1L)
}

fun readInputLine(): String {
    return readLine()!!
}