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 long gcd(long long x,long long y)
{
	return x==0?y:gcd(y%x,x);
}
long long a,b,c,d;
int main()
{
	scanf("%lld%lld%lld%lld",&a,&b,&c,&d);
	long long lcm=c*d/gcd(c,d);
	printf("%lld",(b-a+1)-(b/c-(a-1)/c)-(b/d-(a-1)/d)+(b/lcm-(a-1)/lcm));
	return 0;
}