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 {
	
	static int mod = (int)1e9+7;
	
	public static void main(String[] args) {		
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long A[] = new long[N];
		for(int i=0;i<N;i++)A[i]=sc.nextLong();
		sc.close();

		long ans = 0;
		for(int i=0;i<60;i++) {
			int cnt = 0;
			for(int j=0;j<N;j++) {
				if(((A[j]>>i)&1)==1) cnt++;
			}
			long tmp = (long)cnt*(N-cnt) %mod;
			//ans += tmp<<i;　これだとオーバーフローする?
			long mul = (tmp<<i)%mod;
			//long mul = (long)Math.pow(2, i) % mod;
			ans += (tmp * mul % mod);
			ans %= mod;	
		}
		System.out.println(ans);
	}
	
}