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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
class Program {
    static void Main(string[] args) {
        var N = long.Parse(Console.ReadLine());
        var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        
        var len = Convert.ToString(A.Max(),2).Length;
        var sum1 = new long[len];
        var sum0 = new long[len];
        var til1 = new long[len];
        
        for(long i = N-1;i >= 0;i--){
            var S = Convert.ToString(A[i],2);
            
            for(int j = 0;j < len;j++){
                if(j < S.Length && S[S.Length-j-1] == '1'){
                    til1[j] += sum0[j];
                    sum1[j]++;
                }else{
                    til1[j] += sum1[j];
                    sum0[j]++;
                }
            }
        }
        
        long ans = 0;
        long mo = 1000000007;
        for(int i = 0;i < len;i++){
            //Console.WriteLine(til1[i]);
            ans += (til1[i]%mo)*((long)Math.Pow(2,i)%mo);
            ans %= mo;
        }
        Console.WriteLine(ans);
    }
}