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: Accepted)

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

namespace CSharp_AtCoder
{
    class Program
    {

        const long MOD = 1000000000 + 7;

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            long[] A = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();

            long ans = 0;
            for(int k = 0; k < 60; k++)
            {
                // A の k bit目の1と0の数をカウント
                long ak_0 = 0;
                long ak_1 = 0;
                for(int i = 0; i < N; i++)
                {
                    // A[i]の k bit目の値
                    int ai_k = (int)(A[i] >> k) & 1;

                    if (ai_k == 0) ak_0++;
                    else ak_1++;
                }

                // 2^k 乗を計算
                long k_exp2 = 1;
                for(int j = 0; j < k; j++)
                {
                    k_exp2 *= 2;
                    k_exp2 %= MOD;
                }

                // 1 と 0 の組み合わせは ak_0 * ak_1個
                long sum = (ak_1 * ak_0) % MOD;
                ans += (sum * k_exp2) % MOD;
                ans %= MOD;
            }

            Console.WriteLine(ans);
        }
    }
}