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 (1.15.1) (judge verdict: Accepted)

use std::collections::HashMap;
use std::io::BufRead;

fn main() {
    let stdin = std::io::stdin();
    let (n, a): (usize, i32) = stdin.lock().gets().split(' ').values();
    let xs = stdin.lock().gets().split(' ').take(n)
        .map(|x| x.parse::<i32>().unwrap() - a).collect::<Vec<_>>();
    let mut cnt = HashMap::new();
    cnt.insert(0, 1u64);
    for x in xs.iter() {
        let prev = cnt;
        cnt = HashMap::new();
        for (k, v) in prev.into_iter() {
            *cnt.entry(k).or_insert(0) += v;
            *cnt.entry(k + x).or_insert(0) += v;
        }
    }
    println!("{}", *cnt.entry(0).or_insert(0) - 1);
}

trait Gets { fn gets(&mut self) -> String; }
impl<T: std::io::BufRead> Gets for T {
    fn gets(&mut self) -> String { self.lines().next().unwrap().unwrap() } }

trait Values<T> { fn values(&mut self) -> T; }
impl<'a, I, T1, T2> Values<(T1, T2)> for I
    where I: Iterator<Item=&'a str>,
          T1: std::str::FromStr, T1::Err: std::fmt::Debug,
          T2: std::str::FromStr, T2::Err: std::fmt::Debug {
    fn values(&mut self) -> (T1, T2) {
        (self.next().unwrap().parse().unwrap(),
         self.next().unwrap().parse().unwrap())
    }
}