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 Lua (5.3.2) (judge verdict: Accepted)

function gcd(a,b)
    if b~=0 then
        return gcd(b,a%b)
    else
        return a
    end
end
a,b,c,d=io.read("*n","*n","*n","*n")
x=(b//c+b//d-b//((c*d)//gcd(c,d)))-((a-1)//c+(a-1)//d-(a-1)//((c*d)//gcd(c,d)))
print(b-a+1-x)