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: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD = 1000000007;

ll N,cnt[300000][63],A[300000],sum[63];

int main(void){
    cin >> N;
    rep(i,N){
        cin >> A[i];
        ll x = A[i];
        ll m=0;
        while(x > 0){
            if(x&1==1)cnt[i][m]++;
            x = x>>1;
            m++;
        }
        rep(j,63)sum[j] += cnt[i][j];
        //rep(j,3)cout << sum[j];
        //cout << endl;
    }
    
    ll ans=0;
    rep(i,N){
        ll p=1;
        rep(j,63){
            sum[j]-=cnt[i][j];
            if(cnt[i][j]==0)ans = (ans + (sum[j] *p)%MOD)%MOD;
            else ans = (ans + ( (N -1 - i - sum[j])*p)%MOD)%MOD;
            p = (2 * p)%MOD;
        }
    }
    ans = ans%MOD;
    cout << ans <<endl;
    
}