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)

# ABC131 Anti-devision

def gcd(a, b):
    if b == 0:
        return abs(a)
    return gcd(b, a % b)

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

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

ab_c = B // C - (A - 1) // C
ab_d = B // D - (A - 1) // D
cd_lcm = lcm(C, D)
ab_cd_lcm = B // cd_lcm - (A - 1) // cd_lcm

ans = B - (A - 1) - ab_c - ab_d + ab_cd_lcm

print(ans)