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)

input = gets.chomp
a,b,c,d = input.split.collect{ |item| item.to_i}

result = 0
abmax = b-a+1
cmin = a%c == 0 ? a/c : a/c + 1
cmax = b/c
pop_for_c = cmax - cmin + 1
pop_for_c = 0 if cmin > cmax
dmin = a%d == 0 ? a/d : a/d + 1
dmax = b/d
pop_for_d = dmax - dmin + 1
pop_for_d = 0 if dmin > dmax

cd = c.lcm(d)
cdmin = a%(cd) == 0 ? a/(cd) : a/(cd)+1
cdmax = b/(cd)
plus_for_cd = cdmax - cdmin + 1
plus_for_cd = 0 if cdmin > cdmax

result = abmax - pop_for_c - pop_for_d + plus_for_cd
puts result