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 PyPy3 (2.4.0) (judge verdict: Accepted)

from sys import stdin

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a
  
A,B,C,D = map(int,stdin.readline().rstrip().split())
lcm=(C * D) // gcd(C, D)

AdivLcm=A//lcm
BdivLcm=B//lcm
ABdivLcmNum=BdivLcm-AdivLcm
if A%lcm==0:
  ABdivLcmNum+=1

AdivC = A//C
BdivC = B//C
ABdivCNum = BdivC-AdivC
if A%C==0:
  ABdivCNum+=1

AdivD = A//D
BdivD = B//D
ABdivDNum = BdivD-AdivD
if A%D==0:
  ABdivDNum+=1

candiv=ABdivCNum+ABdivDNum-ABdivLcmNum
print(B-A+1-candiv)