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.Diagnostics;
using System.Linq;

namespace AtCoder.D
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var N = ReadLong();
            var A = ReadLongs();
            var zeroCountByDigits = new long[60];
            var oneCountByDigits = new long[60];

            for (var i = 0; i < N; i++)
            {
                var bit = Convert.ToString(A[i], 2).PadLeft(60, '0');
                for (var j = 0; j < 60; j++)
                {
                    var x = bit[60 - 1 - j];
                    if (x == '0')
                    {
                        zeroCountByDigits[j]++;
                    }
                    else
                    {
                        oneCountByDigits[j]++;
                    }
                }
            }

            var sum = new Modular();
            for (var i = 0; i < 60; i++)
            {
                var pow = (Modular)(long)Math.Pow(2, i);
                sum += pow * zeroCountByDigits[i] * oneCountByDigits[i];
            }

            return sum;
        }

        #region Console

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
        public class Modular
        {
            public long Value { get; private set; }

            private static readonly long _mod = (long)Math.Pow(10, 9) + 7;
            private static readonly List<int> _facCache = new List<int> { 1 };

            public static explicit operator long(Modular m)
            {
                return m.Value;
            }

            public static implicit operator Modular(long a)
            {
                var m = a % _mod;

                return new Modular
                {
                    Value = (m < 0) ? m + _mod : m
                };
            }

            public static Modular operator +(Modular a, Modular b)
            {
                return a.Value + b.Value;
            }

            public static Modular operator -(Modular a, Modular b)
            {
                return a.Value - b.Value;
            }

            public static Modular operator *(Modular a, Modular b)
            {
                return a.Value * b.Value;
            }

            public static Modular operator /(Modular a, Modular b)
            {
                return a * Pow(b, _mod - 2);
            }

            public static Modular Pow(Modular a, long n)
            {
                switch (n)
                {
                    case 0:
                        return 1;
                    case 1:
                        return a;
                    default:
                        var p = Pow(a, n / 2);
                        return p * p * Pow(a, n % 2);
                }
            }
            public static Modular Factorial(long n)
            {
                for (var i = _facCache.Count; i <= n; ++i)
                {
                    var fac = (int)(Math.BigMul(_facCache.Last(), i) % _mod);
                    _facCache.Add(fac);
                }
                return _facCache[(int)n];
            }
            public static Modular Combination(long n, long r)
            {
                Modular ans = 1;
                for (var i = 0; i < r; i++)
                {
                    ans *= n - i;
                }
                for (var i = 1; i <= r; i++)
                {
                    ans /= i;
                }

                return ans;
            }
            public override string ToString()
            {
                return Value.ToString();
            }
        }
    }
}