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)

import Data.List

main = do
    [a,b,c,d] <- map read.words <$> getLine
    putStrLn.show.answer a b c d $ lcm c d

answer a b c d e = (b-a+1) -abc-abd+abe where
    ac_start = if mod a c == 0 then a else a + (c-mod a c)
    bc_end = b - mod b c
    abc = (div bc_end c - div ac_start c + 1)
    ad_start = if mod a d == 0 then a else a + (d-mod a d)
    bd_end = b - mod b d
    abd = (div bd_end d - div ad_start d + 1)
    ae_start = if mod a e == 0 then a else a + (e-mod a e)
    be_end = b - mod b e
    abe = (div be_end e - div ae_start e + 1)