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>

using namespace std; 
#define REP(i, n) for (int i = 0; i < (n); i++)
#define MOD 1000000007LL

typedef long long ll;
int main(int argc, char const *argv[])
{
    cin.tie(0);
   	ios::sync_with_stdio(false);
    ll N; cin >> N;
    vector<int> v(60,0);
    
    ll res = 0;
    REP(i, N){
        ll tmp; cin >> tmp;
        int idx = 0;
        while(tmp > 0) {
            if(tmp % 2) v[idx]++;
            tmp /= 2; idx++; 
        }
    }
    for(ll i = 0; i < 60 ; i++) {
        REP(j, v[i] * (N - v[i])){
            res += (1LL << i) % MOD;
        }
    }
    cout << res%MOD << endl;
    return 0;
}