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;
#define MAX_BIT_NUMBER  62
#define MOD 1000000007LL

long long X, v[MAX_BIT_NUMBER], ans;
int i, n, j;

inline long long M (long long value){
    if (value < MOD)
        return value;
    return value % MOD;
}

long long exp (int k){
    if (!k)
        return 1LL;
    if (k & 1)
        return M(2LL * exp (k - 1));
    long long val = exp (k / 2);
    return M (val * val);
}

int main()
{
    cin >> n;
    for (i = 0; i < n; ++i){
        cin >> X;
        for (j = 0; j < MAX_BIT_NUMBER; ++j)
            if (X & (1LL << j))
            ++v[j];
    }
    for (i = 0; i < MAX_BIT_NUMBER; ++i)
    if (v[i]){
        ans = M (ans + v[i] * (n - v[i]) * exp (i));
    }
    cout << ans;
    return 0;
}