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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;import java.io.*;import java.math.*;
public class Main{
  //↓見なくていいよ！ここから------------------------------------------
  static class InputIterator{
    ArrayList<String> inputLine = new ArrayList<String>(1024);
    int index = 0; int max;
    InputIterator(){
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      while(true){
        String read;
        try{
          read = br.readLine();
        }catch(IOException e){
          read = null;
        }
        if(read != null){
          inputLine.add(read);
        }else{
          break;
        }
      }
      max = inputLine.size();
    }
    boolean hasNext(){return (index < max);}
    String next(){
      if(hasNext()){
        String returnStr = inputLine.get(index);
        index++;
        return returnStr;
      }else{
        throw new IndexOutOfBoundsException("これ以上入力はないよ");
      }
    }
  }
  
  static InputIterator ii = new InputIterator();//リアクティブでは使えないので諦めてScanner使うこと
  static PrintWriter out = new PrintWriter(System.out);
  static void flush(){out.flush();}
  static void myout(Object t){out.println(t);}
  static void myerr(Object t){System.err.println(t);}
  static String next(){return ii.next();}
  static int nextInt(){return Integer.parseInt(next());}
  static long nextLong(){return Long.parseLong(next());}
  static ArrayList<String> nextStrArray(){return myHanSpSplit(next());}
  static ArrayList<String> myHanSpSplit(String str){return new ArrayList<String>(Arrays.asList(str.split(" ")));}
  static ArrayList<String> nextCharArray(){return mySingleSplit(next());}
  static ArrayList<String> mySingleSplit(String str){return new ArrayList<String>(Arrays.asList(str.split("")));}
  static ArrayList<Integer> nextIntArray(){
    ArrayList<Integer> ret = new ArrayList<Integer>();
    ArrayList<String> input = nextStrArray();
    for(int i = 0; i < input.size(); i++){
      ret.add(Integer.parseInt(input.get(i)));
    }
    return ret;
  }
  static ArrayList<Long> nextLongArray(){
    ArrayList<Long> ret = new ArrayList<Long>();
    ArrayList<String> input = nextStrArray();
    for(int i = 0; i < input.size(); i++){
      ret.add(Long.parseLong(input.get(i)));
    }
    return ret;
  }
  static String kaigyoToStr(String[] list){return String.join("\n",list);}
  static String kaigyoToStr(ArrayList<String> list){return String.join("\n",list);}
  static String hanSpToStr(String[] list){return String.join(" ",list);}
  static String hanSpToStr(ArrayList<String> list){return String.join(" ",list);}
  public static void main(String[] args){
    solve();
    flush();
  }
  //↑見なくていいよ！ここまで------------------------------------------
  static void solve(){//ここがメイン関数代わり
    int N = nextInt();
    ArrayList<Long> list = nextLongArray();
    long output = 0;
    final long mod = 1000000007;
    int maxBit = 61;
    HashMap<Integer,HashMap<String, Long>> map = new HashMap<Integer,HashMap<String, Long>>();
    for(int i = 0; i < maxBit; i++){
      HashMap<String, Long> tmp = new HashMap<String, Long>();
      tmp.put("0",new Long("0"));
      tmp.put("1",new Long("0"));
      map.put(i, tmp);
    }
    for(int i = 0; i < N; i++){
      String[] thisCount = new String[maxBit];
      for(int j = 0; j < maxBit; j++){
        thisCount[j] = "0";
      }
      String binaryString = Long.toBinaryString(list.get(i));
      StringBuilder tmp = new StringBuilder();
      for(int j = binaryString.length() - 1; j >= 0 ; j--){
        tmp.append(binaryString.substring(j,j+1));
      }
      binaryString = tmp.toString();
      
      for(int j = 0; j < binaryString.length(); j++){
        thisCount[j] = binaryString.substring(j, j + 1);
      }
      for(int j = 0; j < maxBit; j++){
        HashMap<String, Long> t = map.get(j);
        if(thisCount[j].equals("0")){
          t.put("0", t.get("0") + 1);
        }else{
          t.put("1", t.get("1") + 1);
        }
        map.put(j, t);
      }
    }
    for(int i = 0; i < maxBit; i++){
      HashMap<String, Long> t = map.get(i);
      long one = t.get("0");
      long zero = t.get("1");
      long addCount = zero * one * ((long)Math.pow(2, i) % mod);
      output = (output + addCount) % mod;
    }
    myout(output);
  }
  //Method addition frame start

  //Method addition frame end
}