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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;

#include <math.h>
#define PI 3.14159265358979323846264338327950L

long long gcd(long long a, long long b) {
    if (a == 0)
        return b;
    return gcd(b % a, a);
}
long long lcm(long long a, long long b) {
    return (a * b) / gcd(a, b);
}

int main() {
    cout << (1 << 0);
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; i++) cin >> a[i];
    vector<int> zerobit(61);
    vector<int> onebit(61);
    for (int i = 0; i < n; i++) {
        for (long long bit = 0; bit <= 60; bit++) {
            if (a[i] & ((long long)1 << bit)) onebit[bit]++;
            else zerobit[bit]++;
        }
    }
    long long sum = 0;
    for (int bit = 0; bit <= 60; bit++) {
        sum += ((long long)zerobit[bit] * onebit[bit]) * ((long long)1 << bit); sum %= MOD;
    }
    cout << sum;
    return 0;
}