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;
using LL = long long;
LL gcd(LL a, LL b) {
    return b == 0 ? a : gcd(b, a % b);
}
int main() {
    LL a,b,c,d;
    cin>>a>>b>>c>>d;
    LL lcm=c*d/gcd(c,d);
    a--;
    LL l = a/c+a/d-a/lcm;
    LL r = b/c+b/d-b/lcm;
    cout << (b - r) - (a - l) <<endl; 
}