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)

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

# a以上の最小のbの倍数
def overMinMulti(a, b):
  if a % b == 0:
    return a
  return (a // b + 1) * b

# a以下の最大のbの倍数
def underMaxMulti(a, b):
  return a // b * b

A, B, C, D = map(int, input().split())
E = C * D // gcd(C, D)
print(
  B - A + 1
  - ((underMaxMulti(B, C) - overMinMulti(A, C)) // C + 1)
  - ((underMaxMulti(B, D) - overMinMulti(A, D)) // D + 1)
  + ((underMaxMulti(B, E) - overMinMulti(A, E)) // E + 1)
)