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 <stdio.h>
#include <math.h>
#define ll long long
ll f(ll a,ll b)
{
	return b==0?a:f(b,a%b);
}
int main()
{
	ll m,n,i,j,k,a,b,c,d;
	while(~scanf("%lld%lld%lld%lld",&a,&b,&c,&d))
	{
		m=f(c,d);
		m=c*d/m;
		a-=1;
		n=b-a-(b/c-a/c+b/d-a/d-(b/m-a/m));
		printf("%lld\n",n);
	}
	return 0;
}