PolandBall and Gifts

1000ms

262144K

Description:

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:

Ball number i will bring the present he should give.
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.

Sample Input:

5 2
3 4 1 5 2

Sample Output:

2 4

Sample Input:

10 1
2 3 4 5 6 7 8 9 10 1

Sample Output:

2 2

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.

Informação

Provedor Codeforces

Código CF755F