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?
## Input
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.
## Output
You should output two values — minimum and maximum possible number of Balls who will **not** get their presents, in that order.
[samples]
## Note
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.
圣诞节到了！PolandBall 和他的朋友们将互相赠送礼物。总共有 #cf_span[n] 个 Balls。每个 Ball 都需要根据某个排列 #cf_span[p] 为他人送礼物，其中对所有 #cf_span[i] 都有 #cf_span[pi ≠ i]。
不幸的是，Balls 非常笨拙。我们事先知道，恰好有 #cf_span[k] 个 Ball 会忘记带礼物。Ball #cf_span[i] 能收到礼物，当且仅当满足以下两个条件：
如果恰好有 #cf_span[k] 个 Ball 忘记带礼物，那么最少和最多可能有多少个孩子收不到礼物？
输入的第一行包含两个整数 #cf_span[n] 和 #cf_span[k]（#cf_span[2 ≤ n ≤ 106]，#cf_span[0 ≤ k ≤ n]），分别表示 Balls 的数量和忘记带礼物的 Balls 数量。
第二行包含一个从 #cf_span[1] 到 #cf_span[n] 的排列 #cf_span[p]，其中 #cf_span[pi] 表示第 #cf_span[i] 个 Ball 应该把礼物送给哪个 Ball 的编号。对所有 #cf_span[i]，都有 #cf_span[pi ≠ i]。
你应该输出两个值 —— 收不到礼物的 Balls 的最小和最大可能数量，按此顺序输出。
在第一个样例中，如果第三和第一个 Ball 忘记带礼物，那么只有他们两个收不到礼物。因此最小答案是 #cf_span[2]。然而，如果第一和第二个 Ball 忘记带礼物，那么只有第五个 Ball 能收到礼物。因此最大答案是 #cf_span[4]。
## Input
输入的第一行包含两个整数 #cf_span[n] 和 #cf_span[k]（#cf_span[2 ≤ n ≤ 106]，#cf_span[0 ≤ k ≤ n]），分别表示 Balls 的数量和忘记带礼物的 Balls 数量。第二行包含一个从 #cf_span[1] 到 #cf_span[n] 的排列 #cf_span[p]，其中 #cf_span[pi] 表示第 #cf_span[i] 个 Ball 应该把礼物送给哪个 Ball 的编号。对所有 #cf_span[i]，都有 #cf_span[pi ≠ i]。
## Output
你应该输出两个值 —— 收不到礼物的 Balls 的最小和最大可能数量，按此顺序输出。
[samples]
## Note
在第一个样例中，如果第三和第一个 Ball 忘记带礼物，那么只有他们两个收不到礼物。因此最小答案是 #cf_span[2]。然而，如果第一和第二个 Ball 忘记带礼物，那么只有第五个 Ball 能收到礼物。因此最大答案是 #cf_span[4]。
**Definitions**
Let $ n, k \in \mathbb{Z} $ with $ 2 \leq n \leq 10^6 $, $ 0 \leq k \leq n $.
Let $ p \in S_n $ be a permutation of $ \{1, 2, \dots, n\} $ such that $ p(i) \neq i $ for all $ i $.
Let $ G = (V, E) $ be a directed graph with $ V = \{1, 2, \dots, n\} $ and $ E = \{(i, p(i)) \mid i \in V\} $.
Since $ p $ is a permutation with no fixed points, $ G $ is a disjoint union of directed cycles of length at least 2.
Let $ C_1, C_2, \dots, C_m $ be the cycles in $ G $, with lengths $ \ell_1, \ell_2, \dots, \ell_m \geq 2 $, and $ \sum_{j=1}^m \ell_j = n $.
Let $ F \subseteq V $ be the set of $ k $ Balls who forget to bring gifts, $ |F| = k $.
A Ball $ i $ **does not receive** a gift if and only if the Ball who is supposed to give to $ i $ (i.e., the unique $ j $ such that $ p(j) = i $) is in $ F $.
Let $ R(F) = \{ i \in V \mid p^{-1}(i) \in F \} $ be the set of Balls who do not receive a gift.
**Constraints**
1. $ |F| = k $
2. $ p(i) \neq i $ for all $ i $
3. $ G $ consists of disjoint cycles of length $ \geq 2 $
**Objective**
Compute:
- $ \min_{F \subseteq V, |F|=k} |R(F)| $
- $ \max_{F \subseteq V, |F|=k} |R(F)| $