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: Wrong Answer)

using System;

class Program
{
    static void Main(string[] args)
    {
        string strN = Console.ReadLine();
        Int64 N = Int64.Parse(strN);

        string strArray = Console.ReadLine();
        string[] a_array = strArray.Split(' ');

        Int64[] ai_array = new long[N];

        for (Int64 i = 0; i < N ; i++)
        {
            ai_array[i] = Int64.Parse(a_array[i]);
        }

        Int64 sum = 0;
        for (Int64 i = 0; i < N - 1; i++ )
        {
            for(Int64 j = i + 1; j < N; j++ )
            {
                Int64 xor = ai_array[i] ^ ai_array[j];

                sum += xor;
            }
        }

        Int64 amari = sum % 1000000007;
        Console.WriteLine(amari.ToString());
    }
}