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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program ABC
    implicit none
    integer(8) a, b, c, d, LCM
    read*, a, b, c, d
    a = a - 1
    LCM = c * d / GCD(c, d)
    print"(i0)", ((b - b / c - b / d + b / LCM) - (a - a / c - a / d + a / LCM))
contains
    !GCDを求めるよ！
    recursive integer(8) function GCD (a, b) result (res)
        implicit none
        integer(8) a, b
        if (b > 0) then
            res = GCD(b, mod(a, b))
        else 
            res = a
        end if
    end function
end program ABC