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::*;

fn run() {
    input! {
        n: usize,
        k: usize,
        s: usize,
        t: usize,
        a: [usize; n],
    }
    let a: Vec<usize> = a.into_iter().filter(|a| a & s == s && a | t == t).collect();
    if a.is_empty() || s & t != s {
        println!("0");
        return;
    }
    let mut dp = vec![std::collections::BTreeMap::new(); k + 1];
    dp[0].insert((!0usize, 0usize), 1u64);
    let mut memo = vec![];
    for a in a {
        for i in (0..k).rev() {
            memo.clear();
            for (&(and, or), &cnt) in dp[i].iter() {
                let and = a & and;
                let or = a | or;
                memo.push((and, or, cnt));
            }
            let dp = &mut dp[i + 1];
            for &(and, or, cnt) in memo.iter() {
                *dp.entry((and, or)).or_insert(0) += cnt;
            }
        }
    }
    let mut ans = 0;
    for dp in dp {
        ans += dp.get(&(s, t)).cloned().unwrap_or(0);
    }
    println!("{}", ans);
}

fn main() {
    run();
}