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: Wrong Answer)

integer(8) A,B,C,D,E
integer(8) ans
read*,A,B,C,D
E=C*D/gcd(C,D)
ans=B-A+1

ans=ans-(B-A+1)/C-(B-A+1)/D +(B-A+1)/E
if(mod(B,C)<mod(A,C))ans=ans-1
if(mod(B,D)<mod(A,D))ans=ans-1
if(mod(B,E)<mod(A,E))ans=ans+1

print"(i0)",ans

contains

pure function gcd(a,b)
integer(8),intent(in)::a,b
integer(8) gcd
integer(8) s,t
s=a
gcd=b

t=mod(s,gcd)
do while(t/=0)
  s=gcd
  gcd=t
  t=mod(s,gcd)
end do
end function gcd
end