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>
#include <cstdlib>
using namespace std;

int euclid(int a, int b);

int main()
{
    long int a, b, c, d;
    cin >> a >> b >> c >> d;
    long int div_c, div_d, div_cd;
    div_c = b/c - (a-1)/c;
    div_d = b/d - (a-1)/d;
    div_cd = b/((c*d)/euclid(c, d)) - (a-1)/((c*d)/euclid(c, d));
    cout << b-a+1 - div_c - div_d + div_cd << endl;
    return 0;
}

int euclid(int a, int b){
  if(a%b == 0){
    return b;
  }else{
    return euclid(b, a%b);
  }
}