Feline Friendship

There is a large community of $n$ cats in Delft. The cats are numbered from $1$ to $n$. Each cat has a favourite playing partner $p_i$. Cats can be very egocentric, so $p_i = i$ is allowed. No two cats share the same favourite playing partner, so the $p_i$ are distinct.

You are organising a big game of Cats versus Coatis football, for which you need exactly $k$ cats in a team.

To get $k$ cats to join, you appoint one cat as team captain. Then the following process repeats, starting with the captain. Cat $i$ selects its favourite partner $p_i$ and adds $p_i$ to the team. Then cat $p_i$ selects its favourite partner, adds $p_{p_i}$ to the team, and so on. The process stops only when a cat tries to invite a cat already on the team. If, for some choice of captain, the team has exactly $k$ cats, the game can be played.

Sometimes no team of $k$ cats can be found this way. So you decide to convince some cats to change their favourite playing partner. Formally, you repeatedly select a cat $i$ ($1 \leq i \leq n$), choose $x$ ($1 \leq x \leq n$), and update $p_i := x$. After a change, the $p_i$ may no longer be distinct, which is fine.

What is the minimum number of times you need to convince a cat to change its favourite playing partner so that the game can be played?

Non-American.

The first line contains two integers $n$ and $k$ ($1 \leq n \leq 2 \cdot 10^5$, $1 \leq k \leq n$), the number of cats and the team size. The second line contains $n$ integers $p_1, p_2, \dots, p_n$ ($1 \leq p_i \leq n$), where the $i$th integer is the favourite playing partner of cat $i$. It is guaranteed that the $p_i$ are all distinct.

Output the minimum number of times you need to convince a cat to change its favourite playing partner so that the game can be played.