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;
typedef long long ll;
void Yes(bool Yes){cout << (Yes ? "Yes" : "No") << endl;};
void YES(bool YES){cout << (YES ? "YES" : "NO") << endl;};

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

int main(){

    ll A, B, C, D;
    cin >> A >> B >> C >> D;
    ll W = B - A + 1;
    ll C_OK = B / C - (A - 1) / C;
    ll D_OK = B / D - (A - 1) / D;
    ll CD_OK = B / (lcm(C, D)) - (A - 1) / (lcm(C, D));
    cout << W - C_OK - D_OK + CD_OK << endl;

    return 0;
}