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 ≤ 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.

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