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(){
  long long a,b,c,d;
  cin >> a >> b >> c >> d;
   
  long long divc = b/c - (a-1)/c;
  long long divd = b/d - (a-1)/d;
  
  long long lcm = c*d;
  if(c > d)swap(c,d);
  for(long long i = 1;i*i <= c;i++){
    if(c%i == 0 && d%i == 0)lcm = min(lcm,(c*d)/i);
    if(d%(c/i) == 0 && c%i == 0)lcm = min(lcm,(c*d)/(c/i));
  }
  long long divl = b/lcm - (a-1)/lcm;
  
  cout << (b - a + 1) - (divc + divd - divl) << endl;
}