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

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

N = B - A + 1

g = lcm(C,D)
C_ = B//C - (A-1)//C
D_ = B//D - (A-1)//D
CD_ = B//g - (A-1)//g
ans = N - C_ - D_ + CD_
print(ans)