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;

long long gcd(long long x, long long y)
{
    if (y == 0)
        return x;
    else
        return gcd(y, x % y);
}

int main()
{
    long long a, b, c, d;
    cin >> a >> b >> c >> d;
    a--;
    long long ans = b - b / c - b / d + b / (c * d / gcd(c, d));
    ans -= a - a / c - a / d + a / (c * d / gcd(c, d));
    cout << ans << endl;
}