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 <cstring>
#define ll long long

ll a,b,c,d;
ll gcd(ll x,ll y){return y==0?x:gcd(y,x%y);}
ll solve(ll n)
{
	ll ans=n;
	ans-=n/c;
	ans-=n/d;
	ans+=n/(c*d/gcd(c,d));
	return ans;
}

int main()
{
	scanf("%lld %lld %lld %lld",&a,&b,&c,&d);
	printf("%lld",solve(b)-solve(a-1));
}