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.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class ABC
	{
		static readonly int mod = 1000000007;  // 10^9+7

		static void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });


			int n = int.Parse(Console.ReadLine());
			//string s = Console.ReadLine();
			//int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();

			long[] b = new long[61];
			for (int i = 0; i < n; i++) {
				long x = a[i];
				int j = 0;
				while (x > 0) {
					if (x % 2 == 1) {
						b[j]++;
					}
					x /= 2;
					j++;
				}
			}
			//System.Diagnostics.Debug.WriteLine(string.Join(" ", b));
			long ans = 0;
			for (int i = 0; i < b.Length; i++) {
				ans += b[i] * (n - b[i]) % mod * ((1L << i) % mod);
				ans %= mod;
				//System.Diagnostics.Debug.WriteLine($"{b[i]} * {n - b[i]} * {1L << i:x} % mod");
			}
			Console.WriteLine(ans);


			Console.Out.Flush();
		}
	}
}