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.

Examples

Input

4 9 2 3


Output

2


Input

10 40 6 8


Output

23


Input

314159265358979323 846264338327950288 419716939 937510582


Output

532105071133627368
#include <cstdio>
long long gcd(int x, int y) {
	if (!x) return y;
	if (!y) return x;
	return gcd(y, x%y);
}
int main() {
	long long a, b, c, d;
	scanf("%lld%lld%lld%lld", &a, &b, &c, &d); a--;
	long long l = c*d/gcd(c,d);
	long long ans = b-a+a/c-b/c+a/d-b/d-a/l+b/l;
	printf("%lld\n", ans);
}