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
a,b,c,d = (int(i) for i in raw_input().split())

def lcm(x, y):
    return (x * y) // fractions.gcd(x, y)

def get_num(n, c, d):
    num_of_c = n // c
    num_of_d = n // d
    num_of_cd = n // lcm(c,d)
    ret = n - num_of_c - num_of_d + num_of_cd
    return ret

print get_num(b, c, d) - get_num(a - 1, c, d)