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: Wrong Answer)

import fractions

A, B, C, D = [int(i) for i in input().strip().split()]

# (B - A + 1) - n(C) - n(D) + n(C∩D)

def count_divisible_numbers(x):
  a = (A-1) // 2
  b = B // 2
  return b - a

n_C = count_divisible_numbers(C)
n_D = count_divisible_numbers(D)
CD_lcm = C*D // fractions.gcd(C, D)
n_CD = count_divisible_numbers(CD_lcm)

res = (B - A + 1) - n_C - n_D + n_CD
print(res)