C - Anti-Division

Score : $300$ points

Problem Statement

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 $D$.

4 9 2 3

2

$5$ and $7$ satisfy the condition.

10 40 6 8

23

314159265358979323 846264338327950288 419716939 937510582

532105071133627368