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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using static System.Math;
using static Program.IO.Scanner;
using Number = System.Int64;
using System.Numerics;
#region IO
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;

	public class Printer : StreamWriter {
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	}
	static public class Scanner {
		public static StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
		public static int ri => sc.Integer();
		public static long rl => sc.Long();
		public static string rs => sc.Scan();
		public static double rd => sc.Double();
	}
	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }

		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }

		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) {
				ptr = 0;
				if ((len = str.Read(buf, 0, 1024)) <= 0) {
					isEof = true;
					return 0;
				}
			}
			return buf[ptr++];
		}

		public char Char() {
			byte b = 0;
			do b = read(); while ((b < 33 || 126 < b) && !isEof);
			return (char)b;
		}
		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
		public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
		public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
	}

}

#endregion

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
		return string.Join(st, ie);
	}

	static public void Main() {
		Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
		var solver = new Program.Solver();
		var t = new System.Threading.Thread(solver.Solve, 50000000);
		t.Start();
		t.Join();
		//*/
		//solver.Solve();
		Console.Out.Flush();
	}
}
#endregion

namespace Program {
	public class Solver {
		Random rnd = new Random(0);
		public void Solve() {
			var n = ri;
			var k = ri;
			var S = ri;
			var T = ri;
			if ((S & T) != S || (S | T) != T) {
				Console.WriteLine(0);
				return;
			}
			var a = Enumerate(n, x => ri).Where(x => (x & S) == S).Where(x => (x | T) == T).ToArray();
			n = a.Length;
			const int M = 18;
			long ans = 0;

			var binom = Enumerate(60, x => new long[60]);
			binom[0][0] = 1;
			for (int i = 0; i < 55; i++) {
				for (int j = 0; j < 55; j++) {
					binom[i + 1][j + 1] += binom[i][j];
					binom[i + 1][j] += binom[i][j];
				}
				for (int j = 1; j <= k; j++)
					binom[i][j] += binom[i][j - 1];
			}

			for (int i = 0; i < n; i++) {
				var needZ = 0;
				var needO = 0;
				for (int j = 0; j < M; j++) {
					if ((S >> j & 1) == 0 && (a[i] >> j & 1) == 1) needZ |= 1 << j;
					if ((T >> j & 1) == 1 && (a[i] >> j & 1) == 0) needO |= 1 << j;
				}
				var all = (needO | needZ);
				var cnt = new int[1 << M];
				for (int j = i + 1; j < n; j++) cnt[(a[j] & needO) | ((~a[j]) & needZ)]++;
				for (int j = 0; j < M; j++)
					for (int mask = 0; mask < 1 << M; mask++)
						if ((mask >> j & 1) == 1) cnt[mask] += cnt[mask ^ (1 << j)];
				// Debug.WriteLine(cnt.AsJoinedString());
				var add = 0L;
				for (int mask = 0; mask <= all; mask++) if ((mask | all) == all) {
						// Debug.WriteLine(mask);
						var diff = 0;
						for (int j = 0; j < M; j++)
							if ((mask >> j & 1) != (all >> j & 1)) diff ^= 1;
						var v = binom[cnt[mask]][k - 1];
						if (diff == 0) add += v;
						else add -= v;
					}
				Debug.WriteLine(add);
				ans += add;


			}
			Console.WriteLine(ans);
		}
		const long INF = 1L << 60;
		static int[] dx = { -1, 0, 1, 0 };
		static int[] dy = { 0, 1, 0, -1 };
		static T[] Enumerate<T>(int n, Func<int, T> f) {
			var a = new T[n]; for (int i = 0; i < a.Length; ++i) a[i] = f(i); return a;
		}
		static T[][] Enumerate<T>(int n, int m, Func<int, int, T> f) {
			return Enumerate(n, x => Enumerate(m, y => f(x, y)));
		}
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}