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 a,LL b){return b?Gcd(b,a%b):a;}
inline LL LCM(LL a,LL b){return a/Gcd(a,b)*b;}
inline LL F(LL n){
	return n-n/D-n/C+n/LCM(C,D);
}
int main(){
	cin>>A>>B>>C>>D;
	printf("%lld\n",F(B)-F(A-1));
	return 0;
}
