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 ccc

implicit none
integer(8) :: a, b, c, d, cd, ans

read*, a, b, c, d
call lcm(c,d,cd)

ans=b/c+b/d-b/cd
ans=ans-(a-1)/c-(a-1)/d+(a-1)/cd
ans=(b-a+1)-ans
write(*,'(i0)') ans
end program

subroutine lcm(a,b,res)
integer(8) :: aa, bb, a, b, dumy, i, m, res

aa=a
bb=b

if(a<b) then
dumy=a
a=b
b=dumy
end if

do i = 1, 100000
m=mod(a,b)
if (m==0) then
res=aa*bb/b
a=aa
b=bb
return
else
a=b
b=m
end if
end do

end subroutine lcm