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 math

A, B, C, D = map(int, input().split())

lcm = C * D // math.gcd(C, D)

div_c = (B // C) - (A // C)
if A // C != 0 and A % C == 0:
    div_c += 1
div_d = (B // D) - (A // D)
if A // D != 0 and A % D == 0:
    div_d += 1
div_cd = (B // (lcm)) - (A // (lcm))
if A // (lcm) != 0 and A % lcm == 0:
    div_cd += 1

ans = (B - A + 1) - (div_c + div_d - div_cd)
print(ans)