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: Wrong Answer)

import java.util.*;

public class Main{
	public static void main(String[] $){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		long[]a=new long[n+1];
		int[][]b=new int[60][n+1];
		for(int i=1;i<=n;++i) {
			long v=a[i]=s.nextLong();
			long d=1;
			for(int j=0;j<60;++j,d<<=1)
				b[j][i]=(v&d)>0?1:0;
		}
		for(int[]bb:b)
			Arrays.parallelPrefix(bb,Integer::sum);

		long r=0;
		for(int i=1;i<n;++i) {
			long d=1;
			for(int j=0;j<60;++j,d<<=1) {
				int c=b[j][n]-b[j][i];
				r+=(a[i]&d)>0?(n-i-c)*d:c*d;
				r%=1000000007;
			}
		}

		System.out.println(r);
	}
}