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;
using System.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args) {
#if DEBUG
        //MyDebugger.MakeTestCase("../TextFile2.txt"); return;
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static long mod = 1000000007;

    static object process(TextReader input) {
        var n = int.Parse(input.ReadLine());
        var aa = ToIntArray(input.ReadLine(), n);

        var sum = 0L;

        for(int i=0; i<64; i++) {
            var x = 0L;
            for(int j=0; j<n; j++) {
                x += (aa[j] >> i) % 2;
            }
            sum += (x * (n - x) << i);
            sum %= mod;
        }

        return sum;
    }

    static void print(long list) {
        var buil = new StringBuilder();
        for(int i=0; i<64; i++) {
            buil.Append( (list>>(63-i)) % 2 );
        }
        Debug.Write(buil);
        Debug.WriteLine("(" + list + ")");
    }

    static long[] ToIntArray(string strs, int n) {
        var ret = new long[n];
        var spl =strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = long.Parse(spl[i]);
        return ret;
    }
}