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;
using ll = long long;

int gcd(int a ,int b){
    if(a%b==0) return b;
    else return gcd(b,a%b);
}
ll lcm(int a, int b){
    ll ans = a;
    ans *= b;
    return ans/gcd(a,b);
}


int main(void){
    ll a,b,c,d;
    cin >> a >> b >> c >> d;

    ll ans = b-a+1;
    a--;
    ans -= b/c - a/c;
    ans -= b/d - a/d;
    ans += b/lcm(c,d) - a/lcm(c,d);
    cout << ans << endl;
}