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 fractions


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

    num_C = B // C - (A - 1) // C
    num_D = B // D - (A - 1) // D
    lcm = C * D // fractions.gcd(C, D)
    num_CD = B // lcm - (A - 1) // lcm

    ans = (B - A + 1) - num_C - num_D + num_CD
    print(ans)


if __name__ == '__main__':
    main()