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: Wrong Answer)

#!/usr/bin/env python
from collections import defaultdict
import math
import re

def not_divided(x, A, B):
    if x > B:
        return 0
    if A == B:
        return 1 if A % x == 0 else 0
    lower = math.ceil(A / x)
    upper = math.floor(B / x)
    num = upper - lower + 1
    return num

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

def main():
    A, B, C, D = map(int, input().split())

    if C > D:
        C, D = D, C

    # not divided by C
    C_num = not_divided(C, A, B) 
    D_num = not_divided(D, A, B) 

    CD = C * D // gcd(C, D)
    CD_num = not_divided(CD, A, B)

    C_or_D_num = C_num + D_num - CD_num

    num = (B - A + 1) - C_or_D_num

    print(num)


if __name__ == '__main__':
    main()