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)

# python template for atcoder1
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline


def gcd(a, b):
    """
    最大公約数を求める
    """
    if a < b:
        a, b = b, a
    while b:
        a, b = b, a % b
    return a


def lcm(a, b):
    """
    最小公倍数を求める
    """
    return a*b//(gcd(a, b))


def calc_num(n, C, D):
    """
    0~Nまでで、C or Dで割り切れない数の個数
    """

    div_C = n//C
    div_D = n//D
    div_CD = n//(lcm(C, D))
    return n-div_C-div_D+div_CD


def solve():
    A, B, C, D = map(int, input().split())
    return calc_num(B, C, D)-calc_num(A-1, C, D)


print(solve())