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<iostream>
using namespace std;
int main()
{
    long long a, b, c, d;
    cin >> a >> b >> c >> d;
    
    long long cdiv, ddiv, cddiv;
    long long cd;
  
    cdiv = b/c - a/c;
    if (a % c == 0) cdiv++;
  
    ddiv = b/d - a/d;
    if (a % d == 0) ddiv++;
    
    long long cc = c;
    long long dd = d;
    while (cc != dd) {
      if (cc > dd) {
        cc -= dd;
      } else {
        dd -= cc;
      }
    }
    cd = c * d / cc;
  
    cddiv = b/cd - a/cd;
    if (a % cd == 0) cddiv++;
  
    cout << b-a+1 - (cdiv+ddiv-cddiv) << endl;
    return 0;
}