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>

using namespace std;

long long gcd(long long a, long long b){
    long long r = a % b;
    if(r == 0){
        return b;
    } else {
        return gcd(b, r);
    }
}

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

long long min(long long a, long long b){
    return a < b ? a : b;
}

long long max(long long a, long long b){
    return a > b ? a : b;
}

int main() {
    long long A, B, C, D;

    cin >> A >> B >> C >> D;

    long long min_num = min(C, D);
    long long max_num = max(C, D);
    long long lcm_num = lcm(max_num, min_num);

    long long calc1 = (A - 1) / C + (A - 1) / D - (A - 1) / lcm_num;
    long long calc2 = B / C + B / D - B / lcm_num;

    long long ans = B - (A - 1) - (calc2 - calc1);

    cout << ans << endl;

    return 0;
}