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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

main :: IO ()
main = do
  [a,b,c,d] <- map read . words <$> getLine :: IO [Integer]

  let k = ((c * d) `div` gcd c d)
      l = a `mod` c
      m = a `mod` d
      n = a `mod` k
      l1 = a `div` c
      l2 = b `div` c
      m1 = a `div` d
      m2 = b `div` d
      n1 = a `div` k
      n2 = b `div` k
      l' = l2 - l1 + if l == 0 then 1 else 0
      m' = m2 - m1 + if m == 0 then 1 else 0
      n' = n2 - n1 + if n == 0 then 1 else 0
  print $ (b - a + 1) - (l' + m' - n')