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: Time Limit Exceeded)

from functools import reduce
A, B, C, D = map(int, input().split())

def gcd(*numbers):
    def gcd(a, b):
        while b != 0:
            a, b = b, a % b
        return a
    return reduce(gcd, numbers)

def lcm(*numbers):
    def lcm(a, b):
        return (a * b) // gcd(a, b)
    return reduce(lcm, numbers, 1)

result = 0
while(True):
  if A%C == 0 or A%D == 0:
    A += 1
  else:
    break

result += (B-A+1) - (B//C - A//C) - (B//D - A//D)
l = lcm(C, D)
result += (B//l - A//l)

print("{}".format(result))