Problem A
A Totient Quotient

For a positive integer $k$, Euler’s totient function $\phi (k)$ is defined as the number of positive integers less than or equal to $k$ and relatively prime to $k$. For example, $\phi (9) = 6$, $\phi (24) = 8,$ and $\phi (1) = 1$. (As a reminder, the greatest common divisor (gcd) of two positive integers $a$ and $b$ is the greatest positive integer that divides both $a$ and $b$. Two positive integers are relatively prime if their gcd is $1$.)

Euler’s product formula gives the value of $\phi (k)$ in terms of the prime factorization of $k$. For a prime $p$, let $\nu _p(k)$ be the highest power of $p$ which divides $k$ (so for example, $\nu _2(48) = 4$, $\nu _3(48)=1$, and $\nu _5(48)=0$). If $k$ is a product of powers of prime factors, $k = \prod _{i=1}^j p_i^{\nu _{p_i}(k)}$ (where the product only includes primes $p_i$ with $\nu _{p_i}(k) > 0$), then

A recent edition of The American Mathematical Monthly (Li et al., Positive Rational Numbers of the Form $\phi (m^2)/\phi (n^2)$, 128(2), 2021) proved the following fact about totient quotients: for any pair of positive integers $a$, $b$ there is a unique pair of positive integers $m$, $n$ for which:

1. $\frac{a}{b} = \frac{\phi (m^2)}{\phi (n^2)};$

2. if a prime $p$ divides the product $mn$, then $\nu _p(m) \neq \nu _{p}(n)$;

3. $\gcd (m,n)$ is square-free: that is, for every prime $p$, $\gcd (m,n)$ is not divisible by $p^2$.

Conditions 2 and 3 guarantee that $m$ and $n$ are the unique smallest pair of positive integers satisfying condition 1.

You’d like to verify this claim numerically. Write a program which takes as input two integers $a$ and $b$ and outputs the corresponding pair $m, n$.

Input

The only line of input contains two space-separated integers $a$ and $b$ ($ 1 \leq a, b \leq 10\, 000$). These two integers are guaranteed to be relatively prime. Additionally, $a$ and $b$ will be chosen so that output values $m$ and $n$ are less than $2^{63}$.

Output

Print the two positive integers $m$ and $n$ satisfying all three of the conditions of The American Mathematical Monthly’s theorem, separated by a space. It is guaranteed that $ m, n < 2^{63}$.

9 13

18 13

19 47

13110 18612