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 math

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

def lcm(a,b):
  if a >= b:
    return a*b//gcd(a,b)
  else:
    return a*b//gcd(b,a)


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

k1 = math.ceil(A / C)
k2 = B // C
k3 = math.ceil(A / D)
k4 = B // D

k5 = k2 - k1 + 1
k6 = k4 - k3 + 1

lcm_num = lcm(C, D)
k7 = math.ceil(A / lcm_num)
k8 = B // lcm_num

k9 = k8 - k7 + 1

print(B - A + 1 - k5 - k6 + k9)