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: Time Limit Exceeded)


import java.math.BigInteger;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] list = new int[61];
		for(int i = 0; i < 61; i++) {
			list[i] = 0;
		}
		for(int i = 0; i < n; i++) {
			BigInteger a = new BigInteger(sc.next());
			for(int j = 0; j < 61; j++) {
				if(a.and(new BigInteger("1")).equals(new BigInteger("1"))) {
					list[j]++;
				}
				a = a.divide(new BigInteger("2"));
			}
		}
		BigInteger div = new BigInteger(Long.toString((long) Math.pow(10, 9) + 7));
		BigInteger ans = new BigInteger("0");
		for(int i = 0; i < 61; i++) {
			ans = ans.add(new BigInteger(Integer.toString(list[i])).multiply(new BigInteger(Integer.toString(n - list[i]))).multiply(new BigInteger("2").pow(i).remainder(div)));
			ans = ans.remainder(div);
		}
		System.out.println(ans.toString());

	}

}