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())
num_list = B - A + 1
C_start = int((A/C)+0.99)
C_end = int(B/C)
C_num = C_end - C_start + 1
D_start = int((A/D)+0.99)
D_end = int(B/D)
D_num = D_end - D_start + 1
lcm = C*D/fractions.gcd(C, D)
lcm_start = int((A/lcm)+0.99)
lcm_end = int(B/lcm)
lcm_num = lcm_end - lcm_start + 1
print(num_list-C_num-D_num+lcm_num)