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)

#!/usr/bin/env python3
import sys
try:
    from typing import List
except ImportError:
    pass


def gcd(a: int, b: int):
    if a < b:
        return gcd(b, a)
    while b != 0:
        a, b = b, a % b
    return a


def solve(A: int, B: int, C: int, D: int):
    cdl = C // gcd(C, D) * D
    A -= 1
    print(
        (B - A)
        - (B // C - A // C) - (B // D - A // D)
        + (B // cdl - A // cdl)
    )


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    A = int(next(tokens))  # type: int
    B = int(next(tokens))  # type: int
    C = int(next(tokens))  # type: int
    D = int(next(tokens))  # type: int
    solve(A, B, C, D)


if __name__ == '__main__':
    main()