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 <iostream>

using namespace std;

const long MOD = 1000000007;
typedef pair<int, int> P;
typedef long long ll;

int main(){
    int N;
    cin >> N;
    ll A[N];
    for(int i=0; i<N; i++){
        cin >> A[i];
    }

    ll ans = 0;
    ll mul = 1;
    for(int i=0; i<60; i++){
        ll n0 = 0;
        ll n1 = 0;
        for(int j=0; j<N; j++){
            if(((A[j]>>i) & 1) == 1) n1++;
            if(((A[j]>>i) & 1) == 0) n0++;
        }
        ans = ans + (n1*n0*mul)%MOD;
        ans %= MOD;
        mul = mul*2;
        mul %= MOD;
    }

    cout << ans << endl;

    return 0;
}