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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <cmath>
#include <vector>
#include <queue>
#include <climits>
typedef long long ll;
using namespace std;

int main(void){
  int n,i,j;
  ll mask;
  static ll a[300000];
  const ll mod=1e9+7;

  ll tmp[61]={};
  ll bitsum[61]={};

  cin>>n;
  for(i=0;i<n;i++){
    cin>>a[i];
  }

  mask=1;
  for(j=0;j<61;j++){
    if(a[0]&mask){
      tmp[j]++;
    }
    mask=mask<<1;
  }
  for(i=1;i<n;i++){
    mask=1;
    for(j=0;j<61;j++){
      if(a[i]&mask){
        bitsum[j]+=i-tmp[j];
      }
      else{
        bitsum[j]+=tmp[j];
      }
      mask=mask<<1;
    }

    mask=1;
    for(j=0;j<61;j++){
      if(a[i]&mask){
        tmp[j]++;
      }
      mask=mask<<1;
    }
  }

  ll ans=0;
  mask=1;
  for(i=0;i<61;i++){
    ans+=(bitsum[i]%mod)*(mask%mod);
    ans%=mod;
    mask=mask<<1;
  }

  cout<<ans<<endl;

  return 0;
}