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.

Examples

Input

4 9 2 3


Output

2


Input

10 40 6 8


Output

23


Input

314159265358979323 846264338327950288 419716939 937510582


Output

532105071133627368
import sys

def solve(a, b, c, d):
    c_num = b / c - a / c
    if a % c == 0:
        c_num += 1
    d_num = b / d - a / d
    if a % d == 0:
        d_num += 1

    v = c * d / gcd(c, d)
    v_num = b / v - a / v
    if a % v == 0:
        v_num += 1

    return (b - a + 1) - (c_num + d_num - v_num)


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


if __name__ == '__main__':

    a, b, c, d = map(int, sys.stdin.readline().strip().split(" "))
    print solve(a, b, c, d)