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.*;

 class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        long[] a = new long[(int)N];
        long[] b = new long[105];
        
        for(int i=0;i<N;i++) {
        	a[i] = sc.nextLong();
        	String bin = Long.toBinaryString(a[i]);
//        	System.out.println(bin);
        	for(int j=0;j<bin.length();j++) {
//        		String tmp = bin.substring(j,j+1);
        		if("1".equals(bin.substring(bin.length()-j-1,bin.length()-j))) {
        			b[j]++;
        		}
        	}
        }
        long ans=0;
        for(int i=0;i<100;i++) {
//        	System.out.println(b[i]);
//        	System.out.println(Math.pow(2, i)*b[i]*(N-b[i]));
        	long tmp=b[i]*(N-b[i]);
        	for(int j=0;j<i;j++) {
        		tmp=(tmp*2)%1000000007;
        	}
        	ans = (long) ((ans + tmp)%1000000007);
        }
        System.out.println(ans);	
        
        
    }

}