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 rep(i, n) for(int (i) = 0; i < (n); ++(i))

typedef long long ll;
const ll MOD = 1e9 + 7;

int main() {
  int N;
  std::cin >> N;

  std::vector<ll> A(N);
  rep(i, N) {
    std::cin >> A[i];
  }

  std::vector<ll> X(N);
  std::map<int, int> cnt[2];

  for(int i = N - 1; i >= 0; --i) {
    rep(d, 60) {
      int b = 1LL & (A[i] >> d);
      int c = cnt[1 ^ b][d] % MOD;
      X[i] += (1LL << d) % MOD * c % MOD;
      ++cnt[b][d];
    }
  }

  ll ans = 0;
  rep(i, N - 1) {
    ans += X[i];
    ans %= MOD;
  }
  std::cout << ans << '\n';

}