p02995 AtCoder Beginner Contest 131 - Anti-Division
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
```python
import fractions
a,b,c,d=map(int,input().split())
a-=1
e=c*d//fractions.gcd(c,d)
print(b-a-b//c+a//c-b//d+a//d+b//e-a//e)
```