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>
using namespace std;
using ll = long long;
const ll MOD = (1e+9) +7;

void affect(ll num, vector<ll> &cnt){
    int p = 0;
    while(num != 0){
        cnt[p++] += num%2;
        num /= 2;
    }
}
int main(){
    int n;
    cin >> n;
    vector<ll> a(n);
    vector<ll> cnt(60);
    for(int i=0;i<n;i++){
        cin >> a[i];
        affect(a[i], cnt);
    }
    ll ans = 0;
    for(int i=0;i<n;i++){
        vector<ll> tv(60);
        for(int p = 0;p < 60; p++){
            int b = a[i]%2;
            a[i]/=2;
            cnt[p] -= b;
            ans = (ans + ((ll)pow(2,p)%MOD) * (b?(n-i-1)-cnt[p]:cnt[p]))%MOD;
        }
    }
    cout << (ans%MOD) << endl;
}