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
import math
a,b,c,d=map(int,input().split())
mc = b//c-(a-1)//c
md = b//d-(a-1)//d
cd = (c*d)//math.gcd(c,d)
mcd = b//cd - (a-1)//cd

print(b-a+1 - mc-md+mcd)
