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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
// #define debug(a) cout << "["; rep(i,a.size()) cout << a[i] << ", "; cout<<"]"<< endl;

const ll mod = 1000000007;

//modの世界の2のn乗を返す
ll safe2pow(int n){
    ll ans = 1;
    rep(i,n){
        ans = ans * 2 % mod;
    }
    return ans;
}

int main() {
    int n; cin >> n;
    vector<ll> As(n);
    ll ans = 0;
    rep(i,n) cin >> As.at(i);
    rep(i,60){
        int pi = 0 , qi = 0;
        rep(j,n){
            bitset<60> bs(As.at(j));
            if(bs.test(i)){
                qi++;
            } else {
                pi++;
            }
        }
        ans = (ans + pi * safe2pow(i) % mod * qi) % mod;
    }
    cout << ans << endl;
    return 0;
}