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[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextLong();

		long mod = (long)1e9 + 7;
		long[][] cs = new long[60][n + 1];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < 60; j++)
				cs[j][i] = (a[i] & (1L << j));
		}
		
		for (int i = 0; i < 60; i++)
			for (int j = 1; j <= n; j++)
				cs[i][j] += cs[i][j - 1];

		long ans = 0;
		for (int i = 0; i < n - 1; i++)
			for (int j = 0; j < 60; j++) {
				long cnt = cs[j][n] - cs[j][i];
				if ((a[i] & (1L << j)) == 0) {
					ans += cnt;
					ans %= mod;
				}
				else {
				    long sub = (1L << j) % mod;
				    sub = (sub * (n - 1 - i)) % mod;
					cnt = sub - cnt;
					ans += cnt;
					ans %= mod;
				}
			}
		
		System.out.println(ans);
	}
}