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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class D
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		long[] A = GetLongs((int)N);

		long[] cnt = new long[63];
		for(int i = 0; i < N; i++)
		{
			long rest = A[i];
			for(int j = 0; j <= 62; j++)
			{
				if(rest % 2 == 1)
					cnt[j]++;

				rest >>= 1;
			}
		}

		var P = new ModInt(0);
		for(int i = 0; i <= 62; i++)
		{
			if(cnt[i] == 0)
				continue;

			P += new ModInt((cnt[i] * (cnt[i] - 1)) / 2) * new ModInt(1 << (i + 1));
		}

		var s = new ModInt(0);
		for(int i = 0; i < N; i++)
			s += A[i];

		var Q = s * (N - 1);
		WriteLine((Q - P).Val);
	}
}

public struct ModInt
{
	public long Mod { get; private set; }
	public long Val { get; private set; }

	public ModInt(long v)
	{
		// must initialize (default: Mod = 0)
		Mod = 1000000007;
		Val = v % Mod;
	}

	public static ModInt operator+(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long tmp = x.Val + y.Val;
		if(tmp >= mod)
			tmp -= mod;
		return new ModInt(tmp);
	}


	public static ModInt operator-(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long tmp = x.Val;
		if(tmp < y.Val)
			tmp += mod;
		tmp -= y.Val;
		return new ModInt(tmp);
	}

	public static ModInt operator*(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		return new ModInt((x.Val * y.Val) % mod);
	}

	public static ModInt operator/(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long pow = mod - 2;
		long yy = y.Val;
		long inv = 1;
		while(pow > 0)
		{
			if((pow & 1) == 1)
				inv = (inv * yy) % mod;
			yy = (yy * yy) % mod;
			pow >>= 1;
		}
		return new ModInt((x.Val * inv) % mod);
	}

	public static ModInt operator+(ModInt x, long y) => x + new ModInt(y);
	public static ModInt operator-(ModInt x, long y) => x - new ModInt(y);
	public static ModInt operator*(ModInt x, long y) => x * new ModInt(y);
	public static ModInt operator/(ModInt x, long y) => x / new ModInt(y);
	public static ModInt operator++(ModInt x) => x + new ModInt(1);
	public static ModInt operator--(ModInt x) => x - new ModInt(1);
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}