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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
	input!(n: usize);
	input!(a: usize);
	input!(x: [usize; n]);

	// 0～jまでで、k個使って、sを作れる総数
	let mut dp: Vec<Vec<Vec<usize>>> = vec![vec![vec![0; 3000]; 70]; 70];
	dp[0][0][0] = 1;
	for j in 0..n {
		for k in 0..n {
			for s in 0..50*50 {
				if dp[j][k][s] == 0 {
					continue;
				}
				// 使わない場合
				dp[j+1][k][s] += dp[j][k][s];
				// 使う場合
				dp[j+1][k+1][s+x[j]] += dp[j][k][s];
			}
		}
	}
	// できたDPのうち、条件に合うものを数え上げる。
	// この問題では、カードをi枚選んだとき合計がi*Aになるのが条件(平均がAなので)。
	// 0～Nまでで、i個使って、合計がi*Aになるもの
	let mut ans = 0;
	for i in 1..n+1 {
		ans += dp[n][i][i*a];
	}
	println!("{}", ans);
}