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>
using namespace std;

long long gcd(long long a,long long b)
{
    if(a==0) return b;
    else return gcd(b%a,a);
}

int main()
{
	long long a,b,c,d,e;
	scanf("%lld%lld%lld%lld",&a,&b,&c,&d);
	a--;
	e=c*d/gcd(c,d);
	printf("%lld",b-a-b/c+a/c-b/d+a/d+b/e-a/e);
	return 0;
}