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 <cstdio>
#include <algorithm>
#define ll long long
using namespace std;

ll get(ll l, ll r, ll x) {
	return (r / x - l / x + (l % x == 0 ? 1LL : 0LL));
}

ll gcd(ll a, ll b) {
	while (b) {
		a = a % b;
		swap(a, b);
	}
	return a;
}

int main() {
	ll a, b;
	ll c, d;
	scanf("%lld%lld", &a, &b);
	scanf("%lld%lld", &c, &d);
	ll ans = b - a + 1;
	ans -= get(a, b, c) + get(a, b, d) - get(a, b, c *d / gcd(c, d));
	printf("%lld\n", ans);
	return 0;
}