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.Linq;
using System.Collections.Generic;

namespace ConsoleApp2
{


    public class Program
    {

        static long mod = (long)Math.Pow(10, 9) + 7;

        public static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string[] nString = Console.ReadLine().Split(' ');
            long[] As = new long[N];

            for (int i = 0; i < N; i++)
            {
                As[i] = long.Parse(nString[i]);
            }

            long ans = 0;
            for (int d = 0; d < 60; d++)
            {
                int n0 = 0;
                int n1 = 0;
                for (int i = 0; i < N; i++)
                {
                    long n = As[i]>>d &1;
                    if (n == 0) n0++;
                    if (n == 1) n1++;
                }

                long preAns = n0 * n1;
                for (int i = 1; i <= d; i++)
                {
                    preAns *= 2;
                    preAns %= mod;
                }
                ans += preAns;
                ans %= mod;
            }

            Console.WriteLine(ans);
            Console.ReadLine();

        }

        private static int[] Read(string input)
        {
            string[] strings = input.Split(' ');
            int num = strings.Length;
            int[] ints = new int[num];
            for (int i = 0; i < num; i++)
            {
                ints[i] = int.Parse(strings[i]);
            }
            
            return ints;
        }


    }


}