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: Wrong Answer)

{- A
f :: [Char] -> String
f (x:y:ys)
    | x == y = "Bad"
    | ys == [] ="Good"
    | otherwise = f (y:ys)

main = getLine >>= putStrLn . f
-}


{- B
del :: Int -> Int -> Int -> Int
del d x y
    | d == abs x = y
    | d == abs y = x
    | otherwise = x + y

f :: [Int] -> String
f (n:l:xs) = do
    let x = [l+i-1 | i <- [1..n] ]
    let d = minimum $ map abs x
    show $ foldr1 (del d) x

main = getLine >>= putStrLn . f . map read . words
-}

{- C, TLE
f (a:b:c:d:xs) = length [x | x <- [a..b], x `mod` c /= 0 && x `mod` d /= 0 ]
-}

div2 (a,b) d
    | a <= 1    = b `div` d
    | otherwise = b `div` d - (a - 1) `div` d

f (a:b:c:d:xs)
    | c `mod` d == 0 = b - a + 1 - (a,b) `div2` c
    | d `mod` c == 0 = b - a + 1 - (a,b) `div2` d
    | otherwise      = b - a + 1 - (a,b) `div2` c - (a,b) `div2` d + (a,b) `div2` (lcm c d)

main = getLine >>= putStrLn . show . f . map read . words