Problem J. Jealous Numbers

Author:ACM ICPC 2009-2010, NEERC, Northern Subregional Contest   Time limit:3 sec
Input   Memory limit:256 Mb
Output file:jealous.out  


There is a trouble in Numberland, prime number p is jealous of another prime number q. She thinks that there are more integer numbers between a and b, inclusively, that are divisible by greater power of q than that of p. Help p to get rid of her feelings.

Let α(n, x) be maximal k such that n is divisible by xk. Let us say that a number n is p-dominating over q if α(n, p)>α(n, q). Find out for how many numbers between a and b, inclusive are p-dominating over q.

Input file format

The first line of the input file contains a, b, p and q (1 ≤ a ≤ b ≤ 1018; 2 ≤ p, q ≤ 109; p ≠ q; p and q are prime).

In the given example 3, 9, 15 and 18 are 3-dominating over 2.

Output file format

Output one number — how many numbers n between a and b, inclusive, are p-dominating over q.

Sample tests

No. Input file ( Output file (jealous.out)
1 20 3 2

0.040s 0.012s 15