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.Scanner;
        import java.util.ArrayList;
        import java.util.Collections;
    	import java.util.Arrays;
         
        public class Main { //クラス名はMain
            public static void main(String[] args) {
                //コード
              Scanner sc = new Scanner(System.in);
              int mojilen = sc.nextInt();
              String cw2 = sc.nextLine();  //改行文字空打ち
              String c2 = sc.nextLine();
    		  String[] strArray = c2.split(" ");  
              //文字列リテラル　→　整数変換
              long[] x = new long[(int)strArray.length];
        		for (int k = 0; k < strArray.length; k++) {
            	//x[k] = Integer.parseInt(strArray[k]);
                  x[k] = Long.parseLong(strArray[k]);
        		}
              long wa = 0;
              //計算
              loop: for(int i=0;i<=mojilen-1;i++) {
              	for(int j=i+1;j<=mojilen-1;j++){
                	wa =  wa + (x[i] ^ x[j]); 
              	}
              }
              wa = wa % (long)((long)(Math.pow(10, 9)) + 7);
              System.out.println(wa);
            }
        }