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: Runtime Error)

import sys
from io import StringIO
import unittest
import math


#from numba import jit
def lcm(x, y):
    return (x * y) // math.gcd(x, y)


def resolve():
    A, B, C, D = map(int, input().split())
    size = B - A + 1
    C_warikire = math.ceil(size / C)
    D_warikire = math.ceil(size / D)
    C_and_D_warikire = math.ceil(size / (lcm(C, D)))
    print(size - C_warikire - D_warikire + C_and_D_warikire)
resolve()