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 Python (3.4.3) (judge verdict: Accepted)

A, B, C, D = map(int, input().split())
ans=0

def gcd(m, n):
    x=max(m, n)
    y=min(m, n)
    if x%y == 0:
        return y
    else:
        while x%y!=0:
            z=x%y
            x=y
            y=z
        else:
            return z

def lcm(x, y):
    return (x * y) // gcd(x, y)

lcmCD=lcm(C, D)
ans=B-A+1
ans-=((B//C) - ((A-1)//C))
ans-=((B//D) - ((A-1)//D))
ans+=((B//lcmCD) - ((A-1)//lcmCD))
print(ans)