A10688 | PolandBall and Gifts

It's Christmas time! PolandBall and his friends will be giving themselves gifts. There are $n$ Balls overall. Each Ball has someone for whom he should bring a present according to some permutation $p$ , $p_{i}≠i$ for all $i$ .

Unfortunately, Balls are quite clumsy. We know earlier that exactly $k$ of them will forget to bring their gift. A Ball number $i$ will get his present if the following two constraints will hold:

1. Ball number $i$ will bring the present he should give.
2. Ball $x$ such that $p_{x}=i$ will bring his present.

What is minimum and maximum possible number of kids who will not get their present if exactly $k$ Balls will forget theirs?

The first line of input contains two integers $n$ and $k$ ( $2<=n<=10^{6}$ , $0<=k<=n$ ), representing the number of Balls and the number of Balls who will forget to bring their presents.

The second line contains the permutation $p$ of integers from $1$ to $n$ , where $p_{i}$ is the index of Ball who should get a gift from the $i$ -th Ball. For all $i$ , $p_{i}≠i$ holds.

You should output two values — minimum and maximum possible number of Balls who will not get their presents, in that order.