Problem:
Score : 400 points

Problem Statement

We have N integers. The i-th integer is A_i.

Find \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

2 \leq N \leq 3 \times 10^5

0 \leq A_i < 2^{60}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the value \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

6

We have (1\mbox{ XOR } 2)+(1\mbox{ XOR } 3)+(2\mbox{ XOR } 3)=3+2+1=6.

Sample Input 2

10
3 1 4 1 5 9 2 6 5 3

Sample Output 2

237

Sample Input 3

10
3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820

Sample Output 3

103715602

Print the sum modulo (10^9+7).

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<(n); ++i)
#define rep2(i, s, n) for(int i=s; i<(n); ++i)
#define ALL(v) (v).begin(), (v).end()

using namespace std;

typedef long long ll;

static const int INTINF = (2147483647);
static const ll LLINF = (9223372036854775807);
static const int MAX = 1e5+1;
static const ll MOD = 1e9+7;

namespace Printer{
    template<class T>
    void print(T x){
        cout << x << endl;
    }

    template<class T>
    void print(vector<T> v){
        rep(i, v.size()){
            if(i) cout << " ";
            cout<< v[i];
        }
        cout << endl;
    }

    template<class T>
    void print(vector<vector<T> > vv){
        rep(i, vv.size()){
            rep(j, vv[i].size()){
                if(j) cout << " ";
                cout << vv[i][j];
            }
            cout << endl;
        }
    }

    void print(pair<int, int> p){
        cout << "(" << p.first << ", " << p.second << ")" << endl;
    }
};
using namespace Printer;

//--global--//



//----------//

int main(int argc, const char * argv[]) {
    //提出時、消す----//

    int n;
    cin >> n;
    vector<ll> v(n);
    rep(i, n) cin >> v[i];

    ll ans = 0;
    rep(i, 50){
        ll one = 0;
        ll zero = 0;
        rep(j, n){
            if(v[j] >> i & 1){
                one++;
            }
            else{
                zero++;
            }
        }
        ans += one * zero << i;
        ans %= MOD;
    }

    cout << ans << endl;
    
    
    return 0;
}