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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.lang.*;
public class Main{
	public static long sumXOR(long arr[], int n) 
    { 
    	long mod= (long)1e9+7;
        long sum = 0; 
        for (long i = 0; i < 63; i++)  
        { 
            long zc = 0;  
            long idsum = 0;  
            long k=(long)(1l << i);
            for (int j = 0; j < n; j++) 
            { 
                if ((arr[j]&k)==0) 
                    {zc++;}  
            }             
            k%=mod;
            long x=(long)zc*(n-zc);
            x%=mod;
            idsum = (long) x*k;  
            sum = (long)(sum+idsum)%mod;  
        } 
        return sum; 
    } 
public static void main(String[] args) throws FileNotFoundException, IOException{
       Scanner s=new Scanner(System.in);
      int n=s.nextInt();
      long[] arr=new long[n];
      for(int i=0;i<n;i++){
      	arr[i]=s.nextLong();
      } 	
      long res=sumXOR(arr,n);
      System.out.println(res);
      }
        }