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>
#define ll long long
using namespace std;
ll gcd(ll a,ll b){
	return a%b==0?b:gcd(b,a%b);
}
int main(){
	ll a,b,c,d,e;
	scanf("%lld%lld%lld%lld",&a,&b,&c,&d);
	e=c*d/gcd(c,d);
	a--;
	printf("%lld\n",b-a-(b/d-a/d+b/c-a/c)-a/e+b/e);
	return 0;
}
