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)

# a ~ bでcの倍数の個数を返す
def count_maltiple(a, b, c):
    if a == b:
        if a == b and a%c == 0:
            return 1
        else:
            return 0
    else:
        if a%c == 0:
            st = a
        else:
            st = a + c - a%c

        if (b - b%c) - st < 0:
            return 0
        else:
            return int(((b - b%c) - st)/c + 1)
def gcd( x, y ):
    while y != 0:
        x, y = y, x%y
    return x

def lcm(c, d):
    return c*d // gcd(c,d)


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