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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AC
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var A = ReadArrayLong();
            var cnt = new int[60];
            var mod = 1000000007L;
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < 60; j++)
                {
                    if ((A[i] & 1L << j) == 1L << j)
                    {
                        cnt[j]++;
                    }
                }
            }
            var ans = 0L;
            for (int i = 0; i < N - 1; i++)
            {
                for (int j = 0; j < 60; j++)
                {
                    if ((A[i] & 1L << j) == 1L << j)
                    {
                        cnt[j]--;
                    }
                }
                for (int j = 0; j < 60; j++)
                {
                    var num = (long)Math.Pow(2, j) % mod;
                    if ((A[i] & 1L << j) == 1L << j)
                    {
                        ans += (N - 1 - i - cnt[j]) * num % mod;
                    }
                    else
                    {
                        ans += cnt[j] * num % mod;
                    }
                }
            }

            Console.WriteLine(ans % mod);
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}