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 fractions

f = lambda n, m : n / m
lcm = lambda a, b : a * b / fractions.gcd(a, b)

a, b, c, d = map(int, raw_input().split())
l = lcm(c, d)

a -= 1
a1 = f(a, c) + f(a, d) - f(a, l)
a2 = f(b, c) + f(b, d) - f(b, l)

print (b - a) - (a2 - a1)
