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>
#define USE_MATH_DEFINES
#define rep(i, n) for (int i = 0; i < (n); i++)

using namespace std;

long long gcd(long long m, long long n) {
    if ((0 == m) || (0 == n))
        return 0;

    while (m != n) {
        if (m > n)
            m = m - n;
        else
            n = n - m;
    }
    return m;
}

long long lcm(long long m, int n) {
    if ((0 == m) || (0 == n))
        return 0;

    return ((m / gcd(m, n)) * n);
}

int main() {
    long long a, b, c, d;
    cin >> a >> b >> c >> d;
    long long ans = b - a + 1;
    a -= 1;
    ans -= (b / c - a / c);
    ans -= (b / d - a / d);
    ans += (b / lcm(c, d) - a / lcm(c, d));
    cout << ans << endl;
}