Problem:
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.

Sample Input 1

4 9 2 3

Sample Output 1

2

5 and 7 satisfy the condition.

Sample Input 2

10 40 6 8

Sample Output 2

23

Sample Input 3

314159265358979323 846264338327950288 419716939 937510582

Sample Output 3

532105071133627368

Solution in Ruby (2.3.3) (judge verdict: Accepted)

a, b, c, d = gets.split(" ").map(&:to_i)

g = c.gcd(d)
#print("g=#{g}\n")
bl = b / ((c * d) / g)
al = (a-1) / ((c * d) / g)
#print("bl=#{bl}, al=#{al}\n")
bx = b / c

by = b / d

#x, yの具体的な要素のうち重複するものの個数=i
i = b - bx - by + bl
ax = (a-1) / c

ay = (a-1) / d

j = a-1 - ax - ay + al
#print("i=#{i}, j=#{j}\n")

p i - j