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>
#include <vector>
#define rep(i, n) for (int i = 0; i < (n); i++)
typedef long long ll;
#define MOD 1000000007
using namespace std;

int main(void) {
  ios::sync_with_stdio(false);
  int N;
  cin >> N;
  vector<ll> Zeros(60, 0);
  vector<ll> Ones(60, 0);
  rep(i, N) {
    ll A;
    cin >> A;
    rep(j, 61) {
      if ((A & (1LL << j)) != 0) {
        Ones[j]++;
      } else {
        Zeros[j]++;
      }
    }
  }
  ll SUM = 0;
  rep(i, 61) {
    ll XOR_ONE = (Ones[i] * Zeros[i]) % MOD;
    XOR_ONE = (XOR_ONE << i) % MOD;
    SUM = (SUM + XOR_ONE) % MOD;
  }
  cout << SUM << endl;
  return 0;
}