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>
#include<algorithm>
using namespace std;
#define LL long long
LL a,b,c,d,t;
LL gcd(LL x,LL y){
	if(x==0)return y;
	return gcd(y%x,x);
}
int main(){
	scanf("%lld%lld%lld%lld",&a,&b,&c,&d);t=c*d/gcd(c,d);
	printf("%lld\n",b-a+1-(b/c-(a-1)/c+b/d-(a-1)/d-(b/t-(a-1)/t)));
}