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.*;

public class Main{
  public static void main(String[]args){
    Scanner sc = new Scanner(System.in);
    int N = Integer.parseInt(sc.nextLine());
    String[] S = sc.nextLine().split(" ");
    long[] nums = new long[N];
    long p = 1000000007;
    long ans = 0;
    int s = 0;
    for(int i = 0; i < N; i++){
      nums[i] = Long.parseLong(S[i]);
      String T = Long.toBinaryString(nums[i]);
      s = T.length() > s ? T.length() : s;
    }
    
    long po = 1;
    for(int j = 0; j < s; j++){
      long z = 0, o = 0;
      for(int i = 0; i < N; i++){
        if(nums[i]%2 == 0){
          z++;
        }else{
          o++;
        }
        nums[i] /= 2;
      }
      ans += (((z*o)%p)*po)%p;
      ans %= p;
      po *= 2;
      po %= p;
    }
    System.out.println(ans);
  } 
}