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>
using namespace std;

int mod(int a, int m)
{
    return (a%m + m) % m;
}

int getnumber(){
  int a;
  cin>>a;
  while (!((a < pow(2,60)) && (a >= 0))) {
    exit(0);
  }
  return a;
}
int getn(){
  int a;
  cin>>a;
  while (!((a <= 3* pow(10,5)) && (a >= 2))) {
    exit(0);
  }
  return a;
}
int main(){
  int n;
  n = getn();
  int a[n];
  for(int i=0;i<n;i++){
    a[i]=getnumber();
  }
  int sum = 0;
for(int i=0;i<n-1;i++){
  for(int j=i+1;j<n;j++){
     sum +=  (a[i]^a[j]);


  }
}
  int m = pow(10,9);
  cout<<mod(sum,m)<<endl;
return 0;
}