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)

def gcd(a,b)
  return a if(b==0)
  return gcd(b,a%b);
end

def lcm(a, b)
  return a*b/gcd(a,b);
end

A, B, C, D = gets.strip.split.map {|e| (e.to_i) }
CD = lcm(C,D);

part_c = (B/C - (A-1)/C);

part_d = (B/D - (A-1)/D);

part_cd = (B/CD - (A-1)/CD);

part_c = 0 if(C>B)
part_d = 0 if(D>B)
part_cd = 0 if(CD>B)


result = (B-A+1) - (part_c + part_d - part_cd)

puts result