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