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;


long long int gcd(long long int a, long long int b){ while (a && b){ (a < b) ? b %= a : a %= b; } return a + b; }
long long int lcm(long long int a, long long int b){ return (a / gcd(a, b)) * b; }

int main(){
  long long int A, B, C, D;
  cin >> A >> B >> C >> D;
  cout << B - (B / C + B / D - B / lcm(C, D)) - ((A-1) - ((A-1) / C + (A-1) / D - (A-1) / lcm(C, D))) << endl;
  return 0;
}