Problem:
Score : 300 points

Problem Statement

You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Constraints

1\leq A\leq B\leq 10^{18}

1\leq C,D\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Sample Input 1

4 9 2 3

Sample Output 1

2

5 and 7 satisfy the condition.

Sample Input 2

10 40 6 8

Sample Output 2

23

Sample Input 3

314159265358979323 846264338327950288 419716939 937510582

Sample Output 3

532105071133627368

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
 
int main(void){
  long long A, B, C, D;
  cin >> A >> B >> C >> D;
  long long ABC = B / C - A / C;
  if(A % C == 0) ABC++;
  long long ABD = B / D - A / D;
  if(A % D == 0) ABD++;
  long long L, S, R, X;
  if(C < D){
    L = D;
    S = C;
  }
  else{
    L = C;
  	S = D;
  }

  R = L % S;
  while(R != 0){
   L = S;
    S = R;
    R = L % S;
  }
  X = D * C / S;
  long long ABCD = B / X - A / X;
  if(A % X == 0) ABCD++;
  cout << B - A + 1 - ABC - ABD + ABCD;

  
  
  return 0;
}