Ones

Let $a$ be the natural number whose representation in base $p$ consists of the digit $1$ repeated $n$ times in a row. In other words,

$$a = \underbrace{11\cdots1}{n} = 1 + p + p^2 + \cdots + p^{n-1} = \sum{i=0}^{n-1} p^{i}$$

Find the greatest exponents of $2$ and of $3$ that divide $a$. That is, write a program that finds the largest integer $x$ with $2^{x} \mid a$ and the largest integer $y$ with $3^{y} \mid a$.

The first line contains two natural numbers $p$ and $n$ separated by a space. ($1 < p < 10^9$, $1 \le n < 10^9$)

Print two non-negative integers separated by a space: the greatest exponent $x$ of $2$ that divides $a$, followed by the greatest exponent $y$ of $3$ that divides $a$.