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>
#include <string>
#include <algorithm>
#include <iomanip>
#include <cmath>
#include <vector>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
using lint = long long;
using namespace std;

const int MOD = 1000000007;
const lint INF = 1LL << 60;

const double PI = acos(-1);
const double Rad2Deg = 180.0 / PI;
const double Deg2Rad = PI / 180.0;

int main() {
    int N;
    lint A[300050];
    cin >> N;
    for (int i = 0; i < N; i++) cin >> A[i];

    int d[60];

    lint ans = 0;
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < 60; j++) {
            d[j] += (A[i] >> j) & 1;
        }
    }

    for (int i = 0; i < 60; i++) {
        ans += (1LL << i) * d[i] * (N - d[i]);
    }
    cout << ans % MOD << endl;

    return 0;
}