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)

def gcd(a, b):
    if a<b: a, b = b, a
    while a%b:
        a, b = b, a%b
    return b

def main():
    a, b, c, d = map(int, input().split())
    ans = b - a + 1
    if a%c: ans -= b//c-a//c
    else: ans -= b//c+1-a//c

    if a%d: ans -= b//d-a//d
    else: ans -= b//d+1-a//d

    sks = (c*d) // gcd(c, d)
    if a%sks: ans += b//sks-a//sks
    else: ans += b//sks+1-a//sks
    print(ans)

if __name__=="__main__": main()