CF755F.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?

现在是圣诞节啦！PolandBall 和他的朋友们将互相赠送礼物。一共有 $n$ 个 Ball。每个 Ball 根据某个排列 $p$ 为某个人准备礼物，且对所有 $i$ 均满足 $p_i \neq i$。

不幸的是，这些 Ball 非常笨拙。我们已知恰好有 $k$ 个 Ball 会忘记带自己的礼物。编号为 $i$ 的 Ball 能收到他的礼物，当且仅当以下两个条件同时成立：

1. 编号为 $i$ 的 Ball 带来了他本应送出的礼物；
2. 编号为 $x$ 的 Ball（满足 $p_x = i$）带来了他本应送出的礼物。

如果恰好有 $k$ 个 Ball 忘记带礼物，那么未能收到礼物的 Ball 的最小可能数量和最大可能数量分别是多少？

The first line of input contains two integers n and k (2 ≤ n ≤ 106, 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.

输入的第一行包含两个整数 $n$ 和 $k$（$2 \leq n \leq 10^6$，$0 \leq k \leq n$），分别表示小球的数量以及忘记带礼物的小球数量。

第二行包含一个 $1$ 到 $n$ 的排列 $p$，其中 $p_i$ 表示第 $i$ 个小球本应将礼物送给的小球的编号。对所有 $i$，均有 $p_i \neq i$。

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

你应该输出两个值——无法收到礼物的 Ball 的最小可能数量和最大可能数量，按此顺序输出。

In the first sample, if the third and the first balls will forget to bring their presents, they will be th only balls not getting a present. Thus the minimum answer is 2. However, if the first ans the second balls will forget to bring their presents, then only the fifth ball will get a present. So, the maximum answer is 4.

在第一个样例中，如果第三个球和第一个球忘记带礼物，那么它们将是唯二没有收到礼物的球。因此，最小答案为 2。然而，如果第一个球和第二个球忘记带礼物，则只有第五个球会收到礼物。因此，最大答案为 4。