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: Wrong Answer)

A, B, C, D = $stdin.read.chomp.split(" ").map(&:to_i)

res = B - A + 1

cis = (A / C.to_f).ceil
cie = (B / C.to_f).floor
ccount = if cis == 1 && cie == 0
           0
         else
           cie - cis + 1
         end


dis = (A / D.to_f).ceil
die = (B / D.to_f).floor
dcount = if dis == 1 && die == 0
           0
         else
           die - dis + 1
         end

_gcd = C.gcd(D)
_cd = C*D/_gcd
cdis = (A / (_cd).to_f).ceil
cdie = (B / (_cd).to_f).floor
cdcount = if cdis == 1 && cdie == 0
            0
          else
            cdie - cdis + 1
          end

puts res - ccount - dcount + cdcount