Problem:
Score : 500 points

Problem Statement

Seisu-ya, a store specializing in non-negative integers, sells N non-negative integers. The i-th integer is A_i and has a utility of B_i.
There may be multiple equal integers with different utilities.

Takahashi will buy some integers in this store. He can buy a combination of integers whose bitwise OR is less than or equal to K. He wants the sum of utilities of purchased integers to be as large as possible.

Find the maximum possible sum of utilities of purchased integers.

Constraints

1 \leq N \leq 10^5

0 \leq K < 2^{30}

0 \leq A_i < 2^{30}(1\leq i\leq N)

1 \leq B_i \leq 10^9(1\leq i\leq N)

All input values are integers.

Inputs

Input is given from Standard Input in the following format:

N K
A_1 B_1
:
A_N B_N

Outputs

Print the maximum possible sum of utilities of purchased integers.

Sample Input 1

3 5
3 3
4 4
2 5

Sample Output 1

8

Buy 2 and 3 to achieve the maximum possible total utility, 8.

Sample Input 2

3 6
3 3
4 4
2 5

Sample Output 2

9

Buy 2 and 4 to achieve the maximum possible total utility, 9.

Sample Input 3

7 14
10 5
7 4
11 4
9 8
3 6
6 2
8 9

Sample Output 3

32

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;
class Simple {
    long N, K;
    long[] A, B;
    void Solve() {
        //input
        N = io.Long;
        K = io.Long;
        A = new long[N];
        B = new long[N];
        for (var i = 0; i < N;++i){
            A[i] = io.Long;
            B[i] = io.Long;
        }
        //cal
        var ans = 0L;
        //Kのbitwise_orを変更しない範囲での最大値を求める
        //i番目について調べる
        for (var i = 0; i < N;++i){
            var f = true;
            for (int j = 0; j <= 30;++j){
                //Kの該当するビットが1じゃないのにA[i]の該当するビットが1
                //->bitwise_orを変更してしまうので加えない
                if(((K>>j)&1)==0&&((A[i]>>j)&1)==1){
                    f = false;
                    break;
                }
            }
            if (f)
                ans += B[i];
        }
        //Kのbitwise_orを小さくしたほうが総和が大きくなるかもしれない
        //最終的な形から考える
        //K=5=(101)のとき,(100),(10?),(0??)が他の最終状態として考えられる(?はどっちでもいい)
        for (var i = 0; i <= 30; ++i) {
            //iビットを0に反転して，以降を1にしたK
            if (((K >> i) & 1) == 1) {
                var converted_K = (K & ~(1 << i)) | ((1 << i) - 1);
                var cur = 0L;
                for (int j = 0; j < N; ++j) {
                    var f = true;
                    for (int k = 0; k < 30; ++k) {
                        if (((converted_K >> k) & 1) == 0 && ((A[j] >> k) & 1) == 1) {
                            f = false;
                            break;
                        }
                    }
                    if (f)
                        cur += B[j];
                }
                //更新
                ans = Math.Max(ans, cur);
            }
        }
        //ret
        Console.WriteLine(ans);

    }

    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) { new Simple().Stream(); }
    void Stream() {
        Solve();
        io.writeFlush();
    }
}
class SimpleIO {
    string[] nextBuffer;
    int BufferCnt;
    char[] cs = new char[] { ' ' };
    StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = true };
    public SimpleIO() {
        nextBuffer = new string[0];
        BufferCnt = 0;
        Console.SetOut(sw);
    }
    public string Next() {
        if (BufferCnt < nextBuffer.Length)
            return nextBuffer[BufferCnt++];
        string st = Console.ReadLine();
        while (st == "")
            st = Console.ReadLine();
        nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        BufferCnt = 0;
        return nextBuffer[BufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void writeFlush() { Console.Out.Flush(); }
}