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)

def gcd(a, b)
  if a > b
    return a if b == 0

    gcd(b, a % b)
  else
    return b if a == 0

    gcd(a, b % a)
  end
end

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

num = (B - A + 1)

num_c = B/C - (A-1)/C
num_d = B/D - (A-1)/D

lcm = lcm(C, D)
num_lcm = B/lcm - (A-1)/lcm

# p num_c, num_d, num_lcm

ans = num - num_c - num_d + num_lcm
puts ans