#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll gcd(ll a, ll b) {return b?gcd(b,a%b):a;}
ll lcm(ll a, ll b) {return a/gcd(a,b)*b;}
int main(){
ll a,b,c,d;
cin >>a>>b>>c>>d;
ll cc=b/c-(a-1)/c;
ll dd=b/d-(a-1)/d;
ll k=lcm(c,d);
ll cd=b/k-(a-1)/k;
cout <<b-a+1-cc-dd+cd<<endl;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll gcd(ll a, ll b) {return b?gcd(b,a%b):a;}
ll lcm(ll a, ll b) {return a/gcd(a,b)*b;}
int main(){
ll a,b,c,d;
cin >>a>>b>>c>>d;
ll cc=b/c-(a-1)/c;
ll dd=b/d-(a-1)/d;
ll k=lcm(c,d);
ll cd=b/k-(a-1)/k;
cout <<b-a+1-cc-dd+cd<<endl;
}

```