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 9.2.1) (judge verdict: Wrong Answer)

#pragma region // {{{ by unolight
#include <bits/stdc++.h>
#include <unistd.h>
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wunused-function"
#define SZ(x) ((int)(x).size())
#define ALL(x) begin(x),end(x)
#define RALL(x) rbegin(x),rend(x)
#define REP(i,n) for ( int i=0; i<int(n); i++ )
#define REP1(i,a,b) for ( int i=(a); i<=int(b); i++ )
#define MP make_pair
#define PB push_back
using namespace std;
typedef int64_t LL;
typedef pair<int,int> PII;
typedef vector<int> VI;

namespace { namespace unolight {
// Read Input
template<class T> void _R( T &x ) { cin>>x; }
void _R( int &x ) { scanf("%d",&x); }
void _R( int64_t &x ) { scanf("%" PRId64,&x); }
void _R( double &x ) { scanf("%lf",&x); }
void _R( char &x ) { scanf(" %c",&x); }
void _R( char *x ) { scanf("%s",x); }
void R() {}
template<class T, class... U> void R( T& head, U&... tail ) { _R(head); R(tail...); }
// Write Output
template<class T> void _W( const T &x ) { cout<<x; }
void _W( const int &x ) { printf("%d",x); }
void _W( const int64_t &x ) { printf("%" PRId64,x); }
void _W( const double &x ) { printf("%.16f\n",x); }
void _W( const char &x ) { putchar(x); }
void _W( const char *x ) { printf("%s",x); }
template<class T> void _W( const vector<T> &x ) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W( const T& head, const U&... tail ) { _W(head); putchar(sizeof...(tail)?' ':'\n'); W(tail...); }

#ifdef UNOLIGHT
#include "dump.hpp"
#else
#define dump(...)
#endif

template<class T> inline bool chmax( T &a, const T &b ) { return b>a ? a=b,true : false; }
template<class T> inline bool chmin( T &a, const T &b ) { return b<a ? a=b,true : false; }
template<class T> using MaxHeap = priority_queue<T>;
template<class T> using MinHeap = priority_queue<T, vector<T>, greater<T>>;
template<class T, class F=less<T>> void sort_uniq( vector<T> &v, F f=F() ) {
    sort(begin(v),end(v),f);
    v.resize(unique(begin(v),end(v))-begin(v));
}
#pragma endregion // }}}


void main() {
    int n,k;
    R(n,k);
    VI a(n), b(n);
    REP(i,n) R(a[i],b[i]);
    LL ans=0;
    int cant=0;
    for ( int t=30; ~t; t-- ) {
        LL cur=0;
        if ( k>>t&1 ) {
            cant^=(1<<t);
            REP(i,n) if ( (cant&a[i])==0 ) cur+=b[i];
            cant^=(1<<t);
        } else {
            cant^=(1<<t);
        }
        chmax(ans,cur);
    }
    W(ans);
}

}} // {{{ main
int main() { unolight::main(); return 0; }
// }}}