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):
  while b:
    a, b = b, a % b
  return a
def lcm(x, y):
  return (x * y) // gcd(x, y)
A, B, C, D = map(int, input().split(' '))
can_dived_c = B // C - (A - 1) // C
can_dived_d = B // D - (A - 1) // D
can_dived_both = B // lcm(C, D) - (A - 1) // lcm(C, D)
res = B - (A - 1) - can_dived_c - can_dived_d + can_dived_both
print(res)