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: Accepted)

import math
import fractions

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

a_c = (a - 1) // c
b_c = b // c
a_d = (a - 1) // d
b_d = b // d

lcm = int(c * d / fractions.gcd(c, d))
a_cd = (a - 1) // lcm
b_cd = b // lcm

result = b - a + 1 - (b_c - a_c) - (b_d - a_d) + (b_cd - a_cd)
print(int(result))