Mimi is taking both art and computer science this semester! Inspired, she decides to make an art piece based on the binary representation of two positive integers, $N$ and $M$.

Mimi takes a strip of paper and draws $K$ stripes on it. The $i^{\text{th}}$ stripe is blue if $2^{i-1}$ appears in the binary representation of either $N$ or $M$, but not both. Otherwise, it is painted purple.

Can you tell Mimi how many blue and purple stripes there are?

Constraints

$1\le N,M\le {10}^9$
$1\le K\le 30$

Input Specification

The first and only line of input will contain 3 space separated integers: $N$, $M$, and $K$.

Output Specification

The output should contain two space-separated integers: the number of stripes that are painted blue, and the number of stripes that are painted purple, respectively.

Sample Input

3 1 2

Sample Output

1 1

Explanation for Sample Output

The binary representation of $3$ is $2^1+2^0$, and the binary representation of $1$ is $2^0$.
Both representations have $2^0$, so the first stripe is painted purple.
Since only $3$ has $2^1$ in its binary representation, the second stripe is painted blue.