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.ComponentModel.Design;
using System.Diagnostics;
using System.Linq;
using System.Runtime;
using System.Text;
using Microsoft.Win32;
using static System.Console;
 
 public static class Program
 {
     private static readonly long INF = long.MaxValue / 2;
     private static readonly int MOD = 1000000007;
 
     struct Pair<T, U> : IComparable<Pair<T, U>>
         where T : IComparable<T>
         where U : IComparable<U>
     {
         public T first;
         public U second;
         private bool CompWithFirst;
 
         public Pair(T f, U s, int comp)
         {
             first = f;
             second = s;
             CompWithFirst = comp == 1;
         }
 
         public int CompareTo(Pair<T, U> other)
         {
             return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
         }
     }
 
     public class PriorityQueue<T> where T : IComparable<T>
     {
 
         private List<T> Q;
         private readonly int r;
 
         public PriorityQueue(bool ascending)
         {
             if (ascending)
             {
                 r = 1;
             }
             else
             {
                 r = -1;
             }
 
             Q = new List<T>();
         }
 
 
         private void PushHeap(List<T> list, T item)
         {
             int n = list.Count();
             list.Add(item);
 
             while (n != 0)
             {
                 int pIndex = (n - 1) / 2;
 
                 if (list[n].CompareTo(list[pIndex]) * r > 0)
                 {
                     Swap(Q, n, pIndex);
                 }
                 else
                 {
                     break;
                 }
 
                 n = pIndex;
             }
         }
 
         private void PopHeap(List<T> list)
         {
             int n = list.Count() - 1;
             list[0] = list[n];
             list.RemoveAt(n);
 
             int cur = 0;
             int comp;
 
             while (2 * cur + 1 <= n - 1)
             {
                 int c1 = 2 * cur + 1;
                 int c2 = 2 * (cur + 1);
                 if (c1 == n - 1)
                 {
                     comp = c1;
                 }
                 else
                 {
 
                     comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                 }
 
                 if (list[cur].CompareTo(list[comp]) * r < 0)
                 {
                     Swap(Q, cur, comp);
                 }
                 else
                 {
                     break;
                 }
 
                 cur = comp;
             }
         }
 
         private void Swap(List<T> list, int a, int b)
         {
             T keep = list[a];
             list[a] = list[b];
             list[b] = keep;
         }
 
 
 
         public void Enqueue(T value)
         {
             PushHeap(Q, value);
         }
 
         public T Dequeue()
         {
             T ret = Q[0];
             PopHeap(Q);
             return ret;
         }
 
         public T Peek()
         {
             return Q[0];
         }
 
         public int CountItem()
         {
             return Q.Count();
         }
 
         public bool IsEmpty()
         {
             return !Q.Any();
         }
     }
 
     static long ModInv(long a, long m)
     {
         long b = m, u = 1, v = 0;
         while (b != 0)
         {
             long t = a / b;
             a -= t * b;
             long tmp = a;
             a = b;
             b = tmp;
             u -= t * v;
             tmp = u;
             u = v;
             v = tmp;
         }
 
         u %= m;
         if (u < 0) u += m;
         return u;
     }
 
     public static long CalcComb(long n, long m)
     {
         //条件チェック
         if (n < m) return 0;
         if (n < 0 || m < 0) return 0;
 
         //nＣm ＝ nＣm-1 ×（n-m+1）/ m 
 //         return CalcFact(n) / (CalcFact(m) * CalcFact(n - m));
         //MODで割ってbの逆元を求める
         return CalcFact(n) * ModInv((CalcFact(m) * CalcFact(n - m)) % MOD, MOD) % MOD;
     }
 
     /// <summary>
     /// 階乗を計算する。
     /// </summary>
     /// <param name="n">n</param>
     /// <returns>nの階乗（n!）</returns>
     public static long CalcFact(long n)
     {
         if (n <= 0)
         {
             return 1;
         }
 
         return n * CalcFact(n - 1) % MOD;
     }
 
 
     struct Pos
     {
         public int x;
         public int y;
 
         public Pos(int x, int y)
         {
             this.x = x;
             this.y = y;
         }
         
         public static Pos operator +(Pos p1, Pos p2)
         {
             var result = new Pos();
             result.x = p2.x + p1.x;
             result.y = p2.y + p1.y;
             return result;
         }
 
         public static Pos operator -(Pos p1, Pos p2)
         {
             var result = new Pos();
             result.x = p2.x - p1.x;
             result.y = p2.y - p1.y;
             return result;
         }
     }
     
     class Modular
     {
         private const int M = 1000000007;
         private long value;
 
         public Modular(long value)
         {
             this.value = value;
         }
 
         public static implicit operator Modular(long a)
         {
             var m = a % M;
             return new Modular((m < 0) ? m + M : 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;
         }
 
         private static Modular Pow(Modular a, int 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 operator /(Modular a, Modular b)
         {
             return a * Pow(b, M - 2);
         }
 
         private static readonly List<int> facs = new List<int> {1};
 
         private static Modular Fac(int n)
         {
             for (int i = facs.Count; i <= n; ++i)
             {
                 facs.Add((int) (Math.BigMul(facs.Last(), i) % M));
             }
 
             return facs[n];
         }
 
         public static Modular Ncr(int n, int r)
         {
             return (n < r) ? 0
                 : (n == r) ? 1
                 : Fac(n) / (Fac(r) * Fac(n - r));
         }
 
         public static explicit operator int(Modular a)
         {
             return (int) a.value;
         }
     }
     
     static class Permutation<T>
     {
         private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
         {
             int N = a.Length;
             if (N == 0)
             {
                 perms.Add(stack.Reverse().ToArray());
             }
             else
             {
                 var b = new T[N - 1];
                 Array.Copy(a, 1, b, 0, N - 1);
                 for (int i = 0; i < a.Length; ++i)
                 {
                     stack.Push(a[i]);
                     Search(perms, stack, b);
                     if (i < b.Length) { b[i] = a[i]; }
                     stack.Pop();
                 }
             }
         }
         public static IEnumerable<T[]> All(IEnumerable<T> src)
         {
             var perms = new List<T[]>();
             Search(perms, new Stack<T>(), src.ToArray());
             return perms;
         }
     }
 
     public static int ReadLineToInt()
     {
         return int.Parse(ReadLine());
     }
     
     public static long ReadLineToLong()
     {
         return long.Parse(ReadLine());
     }
     
     public static int[] ReadLineToInts()
     {
         return ReadLine().Split(' ').Select(int.Parse).ToArray();
     }
     
     public static long[] ReadLineToLongs()
     {
         return ReadLine().Split(' ').Select(long.Parse).ToArray();
     }
     
     static int nibunn(int[] array, int target)
     {
         int L = 0;
         int R = array.Length; 
             
         while(R - L > 1)
         {
             int mid = (R + L) / 2;
             if (array[mid] > target) L = mid;
             else R = mid;
         }
         return L;
     }


     struct Testmony
     {
         public int To;
         public int IsHonest;

         public Testmony(int to, int isHonest)
         {
             To = to;
             IsHonest = isHonest;
         }
     }
     
     public static void Main(string[] args)
     {
         int n = ReadLineToInt();
         long[] v = ReadLineToLongs();
         long ans = 0;
         for (int i = 0; i < 60; i++)
         {
             long x = 0;
             foreach (var e in v)
                 if ((e >> i & 1) == 1)
                     x++;
             long xy = x * (n - x) % MOD;
             for (int j = 0; j < i; j++)
             {
                 xy = 2 * xy % MOD;
             }

             ans += xy;
             ans %= MOD;
         }
         WriteLine(ans);
     }
 }