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>
typedef long long ll;
ll gcd(ll p,ll q)
{
    if(q==0)
        return p;
    return gcd(q,p%q);
}
int main(void)
{
    ll a,b,c,d;
    scanf("%lld %lld %lld %lld" ,&a,&b,&c,&d);
    a--;
    ll l=c*d/gcd(c,d);
    printf("%lld" ,b-(b/c+b/d-b/l)-(a-(a/c+a/d-a/l)));
    return 0;
}
