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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace No1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = Convert.ToInt32( Console.ReadLine());
            string str = Console.ReadLine();
            string[] strs = str.Split(' ');
            ulong[] num = new ulong[(int)1e6];
            ulong sum = 0, tem = (Int64)1e9 + 7;
            for (var i = 0; i < strs.Length; i++)
            {
                num[i] = ulong.Parse(strs[i]);
               
            }
            ulong nums = 1;
            for (var i = 0; i < 64; i++)
            {
                int zero = 0, one = 0;
                for (var j=0;j<n;j++)
                {
                    if (num[j] % 2 == 1)
                        one++;
                    else
                        zero++;
                    num[j] = num[j] >> 1;
                }
                int b = zero * one;
                
                //Console.WriteLine(zero+" "+one+" "+nums);
                sum = (sum + ((ulong)b *nums)%tem)%tem;
                nums = (nums << 1) % tem;

            }
            Console.WriteLine(sum%tem);

        }
    }
}