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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

long int expon2(int n);

void seq_reflesh(long int K, unsigned short int *seq);

int main(void){
  long int N, K, i, score, mscore;//scoreがオーバー風呂しないかやや心配
  unsigned short int seq[30];
  int j, bits, m, first;

  scanf("%ld %ld", &N, &K);

  long int list[N][2];

  for(i = 0; i < N; i++){
    scanf("%ld %ld", &list[i][0], &list[i][1]);
  }

  //A_iは最大30ビット

  //立ってるビットの数　＋　1だけ候補がある（最大31
  

  first = 1;
  do{
    seq_reflesh(K, seq);
    score=0;
    //これをKとしてまずがんばる
    for(i=0; i<N;i++){
      if((K | list[i][0]) == K) score = score + list[i][1];
    }
    if(first || mscore < score){
      mscore = score;
    }
    //ここからKの下を取り崩す処理
    m = 0;
    while(seq[m]){
      m++;
    }//mは初めて0になる桁でとまる

    if(expon2(m) > K) break;
    else{
      while(!seq[m]) m++;//mが再び1になったら止まる
    }

    K = K - expon2(m);

    K = K | (expon2(m) - 1);

    first = 0;
  } while(1);

  printf("%ld\n", mscore);
  return 0;
}

long int expon2(int n){
  long int result=1;
  int i;
  for(i=0;i<n;i++) result = result * 2;
  return result;
}

void seq_reflesh(long int K, unsigned short int *seq){
  long int exp;
  int j;
  
  exp = expon2(30);
  //exp=2^30

  
  for(j=29;j>=0;j--){
    exp = exp / 2;
    if(exp & K) seq[j] = 1; //2^j and Kが0じゃなければ
    else seq[j] = 0;
  }
}