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)

if C<D
  n,m = C,D 
else 
  n,m = D,C
end
while m%n != 0
  n,m = m%n, n
end

lcm = C*D/n

p B - A + 1 - ((B/C)-((A-1)/C)) - ((B/D)-((A-1)/D)) + ((B/lcm)-((A-1)/lcm))