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>

long long gcd(long long a, long long b) {
    long long r = a % b;
    return r ? gcd(b, r) : b;
}

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

int main() {
    long long A, B, C, D;
    std::cin >> A >> B >> C >> D;

    long long E = lcm(C, D);

    long long ans = B - A + 1;
    ans -= B / C - (A - 1) / C;
    ans -= B / D - (A - 1) / D;
    ans += B / E - (A - 1) / E;
    std::cout << ans << "\n";
}