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>
#include <boost/multiprecision/cpp_int.hpp>

using boost::multiprecision::cpp_int;
using namespace std;

#if __has_include("print.hpp")
  #include "print.hpp"
#endif

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define MOD 1000000007

typedef long long ll;
typedef pair<ll, ll> p;


int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<ll> v(n);
  rep(i, n) cin >> v[i];
  ll res = 0;

  vector<ll> count(100);

  for (int i = 0; i < n; i++) {
    // while(tmp < v[i]){
    //   tmp *= 2;
    //   ci++;
    // }
    int index = 0;
    while(v[i] > 0){
      if(v[i] % 2 == 1) count[index]++;
      v[i] /= 2;
      index++;
    }
  }

  for (int i = 0; i < 100; i++) {
    res += (count[i] * (n-count[i]) % MOD) * (ll(pow(2, i)) % MOD);
    res %= MOD;
  }
  cout << res << endl;

}