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: Runtime Error)

from sys import stdin
import math


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


def main():
    A, B, C, D = [int(x) for x in stdin.readline().rstrip().split()]

    C_D_lcm = lcm(C, D)

    z = B//C_D_lcm - A//C_D_lcm

    if A % C == 0:
        x = (B//C)+1 - (A//C)
    else:
        x = (B//C) - A//C

    y = B//D - A//D

    print((B-A+1)-(x+y-z))


if __name__ == "__main__":
    main()