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;
using pii = pair<int, int>;



ll A, B, C, D;

ll gcd(ll a, ll b){
    if(b == 0) return a;
    return gcd(b, a % b);
}

ll lcm(ll a, ll b){
    return a * b / gcd(a, b);
}

ll ans(ll num){
    if(num == 0) return 0;

    ll c = num / C;
    ll d = num / D;
    ll cd = num / lcm(C, D);
    
    return num - c - d + cd;
}


int main(){
    
    cin >> A >> B >> C >> D;
    cout << ans(B) - ans(A - 1) << endl;

    return 0;
}