Problem:
Score : 800 points

Problem Statement

Given are N pairwise distinct non-negative integers A_1,A_2,\ldots,A_N.
Find the number of ways to choose a set of between 1 and K numbers (inclusive) from the given numbers so that the following two conditions are satisfied:

The bitwise AND of the chosen numbers is S.

The bitwise OR of the chosen numbers is T.

Constraints

1 \leq N \leq 50

1 \leq K \leq N

0 \leq A_i < 2^{18}

0 \leq S < 2^{18}

0 \leq T < 2^{18}

A_i \neq A_j (1 \leq i < j \leq N)

Input

Input is given from Standard Input in the following format:

N K S T
A_1 A_2 ... A_N

Output

Print the answer.

Sample Input 1

3 3 0 3
1 2 3

Sample Output 1

2

The conditions are satisfied when we choose \{1,2\} or \{1,2,3\}.

Sample Input 2

5 3 1 7
3 4 9 1 5

Sample Output 2

2

Sample Input 3

5 4 0 15
3 4 9 1 5

Sample Output 3

3

Solution in Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::collections::HashMap;

fn main() {
    input! {
        n: usize, k: usize, s: usize, t: usize,
        a: [usize; n]
    }
    let mut dp = vec![HashMap::new(); k + 1];
    dp[0].insert(((1 << 18) - 1, 0), 1);
    for &a in &a {
        for i in (0..k).rev() {
            let mut ins = Vec::new();
            for (&(x, y), &p) in &dp[i] {
                let x = x & a;
                let y = y | a;
                if x & s != s || y | t != t {
                    continue;
                }
                ins.push(((x, y), p));
            }
            for (xy, p) in ins {
                *dp[i + 1].entry(xy).or_insert(0) += p;
            }
        }
    }
    let ans: u64 = (1..=k).filter_map(|i| dp[i].get(&(s, t))).sum();
    println!("{}", ans)
}