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>
#define MOD 1000000007

using namespace std;

long long solve() {
  int N;
  cin >> N;

  vector<long long> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }

  vector<vector<long long>> C(N + 1, vector<long long>(63, 0));
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < 63; j++) {
      if (A[i] & ((long long) 1 << j)) {
        C[i+1][j] = C[i][j] + 1;
      } else {
        C[i+1][j] = C[i][j];
      }
    }
  }

  long long ans = 0;
  for (int i = 0; i < N - 1; i++) {
    for (int k = 0; k < 63; k++) {
      long long c = C[N][k] - C[i+1][k];
      if (A[i] & ((long long) 1 << k)) {
        c = (long long) (N - i - 1) - c;
      }
      c = c % MOD;
      ans += ((((long long) 1 << k) % MOD) * c) % MOD;
      ans = ans % MOD;
    }
  }
  return ans % MOD;
}

int main() {
  cout << solve() << endl;
  return 0;
}