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::fastout;
use whiteread::parse_line;

#[fastout]
fn main() {
    let (_, a): (usize, usize) = parse_line().unwrap();
    let x: Vec<usize> = parse_line().unwrap();

    let mut plus = vec![];
    let mut minus = vec![];
    for v in x {
        if v >= a {
            plus.push(v - a);
        } else {
            minus.push(a - v);
        }
    }

    let mut dp_plus: Vec<Vec<usize>> = vec![vec![0; 2501]; plus.len() + 1];
    let mut dp_minus: Vec<Vec<usize>> = vec![vec![0; 2501]; minus.len() + 1];
    // for _ in 0..(n + 1) {
    //     let mut v = vec![];
    //     v.resize(2501, 0);
    //     dp_plus.push(v);
    //     let mut v = vec![];
    //     v.resize(2501, 0);
    //     dp_minus.push(v);
    // }
    dp_plus[0][0] = 1;
    dp_minus[0][0] = 1;

    for i in 1..(plus.len() + 1) {
        for j in 0..2501 {
            if j >= plus[i - 1] {
                dp_plus[i][j] = dp_plus[i - 1][j] + dp_plus[i - 1][j - plus[i - 1]];
            } else {
                dp_plus[i][j] = dp_plus[i - 1][j];
            }
        }
    }
    for i in 1..(minus.len() + 1) {
        for j in 0..2501 {
            if j >= minus[i - 1] {
                dp_minus[i][j] = dp_minus[i - 1][j] + dp_minus[i - 1][j - minus[i - 1]];
            } else {
                dp_minus[i][j] = dp_minus[i - 1][j];
            }
        }
    }

    let mut ret = dp_plus.last().unwrap()[0];
    for i in 1..2501 {
        ret += dp_plus.last().unwrap()[i] * dp_minus.last().unwrap()[i];
    }
    ret -= 1;
    println!("{}", ret);
}