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 <bits/stdc++.h>
using namespace std;

long gcd(long a, long b) {
	while (b) swap(a %= b, b);
	return a;
}
int main() {
	long a, b, c, d;
	cin >> a >> b >> c >> d;
	long l = c * d / gcd(c, d);
	a--;
	cout << b - (b / c + b / d - b / l) - a + (a / c + a / d - a / l) << endl;
	return 0;
}
