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.Scanner;

public class Main {
	static final int maxBinary = 60;
	static long[] pow2 = new long[60];
	static{
		long n = 1;
		for(int i = 0; i < maxBinary; i++){
			pow2[i] = n;
			n *= 2;
		}
	}
	static long mod = 1_000_000_007;
	static boolean[] toBinary(long l){
		boolean[] ary = new boolean[60];
		for(int i = 0; i < 60 ; i++){
			ary[i] = l / pow2[i] % 2 == 1;
		}
		return ary;
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		boolean[][] binaryArys = new boolean[n][];
		for(int i = 0; i < n; i++){
			binaryArys[i] = toBinary(sc.nextLong());
		}
		long sum = 0;
		for(int i = 0; i < maxBinary; i++){
			int trueNum = 0;
			int falseNum = 0;
			for(int k = 0; k < n; k++){
				if(binaryArys[k][i]){
					trueNum++;
				}else{
					falseNum++;
				}
			}
			sum += (trueNum * (falseNum * (pow2[i] % mod) % mod)) % mod;
			sum %= mod;
		}
		System.out.println(sum);
	}
}