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 PyPy3 (2.4.0) (judge verdict: Accepted)

a, b, c, d = map(int, input().split())
all_count = b - a + 1

def f(x, y, z):
    cnt = y // z - x // z
    if x % z == 0:
        cnt += 1
    return cnt

div_c_count = f(a, b, c)
div_d_count = f(a, b, d)

import fractions
lcm = c * d // fractions.gcd(c, d)
cm_count = f(a, b, lcm)

print(all_count - (div_c_count + div_d_count - cm_count))