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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace ABC147D
{
    class Program
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            long[] A = new long[N];
            string[] Ainput = Console.ReadLine().Split(' ');
            for(int i = 0; i < N; i++)
            {
                A[i] = long.Parse(Ainput[i]);
            }
            long[] zero = new long[60];
            long[] one = new long[60];
            for(int i = 0; i < N; i++)
            {
                string s = Convert.ToString(A[i], 2);
                int l = s.Length;
                //Console.WriteLine(s);
                for(int j = 0; j < l; j++)
                {
                    if (s[l - j - 1].ToString() == "1")
                    {
                        one[j] += 1;
                    }
                    else
                    {
                        zero[j] += 1;
                    }
                }
                if (l < 60)
                {
                    for (int j = l; j < 60; j++)
                    {
                        zero[j] += 1;
                    }
                }
            }
            long m = 1;
            long ans = 0;
            for(int i = 0; i < 60; i++)
            {
                long a = zero[i] * one[i];
                a %= 1000000007;
                ans += a*m;
                ans %= 1000000007;
                m *= 2;
                m %= 1000000007;
            }
            //Console.WriteLine(string.Join("",zero));
            //Console.WriteLine(string.Join("", one));
            Console.WriteLine(ans);
        }
    }
}