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 fractions
a, b, c, d = map(int, input().split())
ans = 0

def lcm(x, y):
    return (x * y) // fractions.gcd(x, y)

k = b-a+1

amri_c = a % c
if amri_c == 0:
    amri_c = c
    k_c = (k - (amri_c - 1)) // c
else:
    k_c = (k - (amri_c - 1)) // c + 1

amri_d = a % d
if amri_d == 0:
    amri_d = d
    k_d = (k - (amri_d - 1)) // d
else:
    k_d = (k - (amri_d - 1)) // d + 1

amri_cd = a % lcm(c, d)
if amri_cd == 0:
    amri_cd = lcm(c, d)
    k_cd = (k - (amri_cd - 1)) // lcm(c, d)
else:
    k_cd = (k - (amri_cd - 1)) // lcm(c, d) + 1

ans = k-k_c-k_d+k_cd

print(ans)