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 <bits/stdc++.h>
#include <iostream>
//#include <algorithm>
// #include <iomanip>
#define ll unsigned long long

using namespace std;

const ll MOD = 1000000007;

ll BITS[64];

int main() {
  int n;
  scanf("%d", &n);

  int zero[64];
  int one[64];
  memset(zero, 0, sizeof(zero));
  memset(one, 0, sizeof(one));
  ll ONE = 1;

  for (int i = 0; i < 64; i++) {
    BITS[i] = (ONE << i);
  }

  for (int i = 0; i < n; i++) {
    ll v;
    scanf("%lld", &v);

    for (int j = 0; j < 64; j++) {
      if (v & (BITS[j])) {
        one[j]++;
      }
      if ((~v) & (BITS[j])) {
        zero[j]++;
      }
    }
  }

  ll ans = 0;

  for (int i = 0; i < 64; i++) {
    int x = zero[i] * one[i];
    for (int j = 0; j < x; j++) {
      ans = (ans + BITS[i]) % MOD;
    }
  }

  cout << ans << endl;
}