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Alien Peter wants to trace his family pedigrees. Working hard for several weeks, he has created a beta-version of his family tree. Unfortunately, some of his ancestors have too much parents in this tree (aliens have d parents). So Peter thinks that some of parent-child relations actually are ancestor-descendant relations. Now Peter wants to know, what minimal number of ancestors need to be added to the tree to make it look well-formed (family tree looks well-formed if each alien has no more than d parents, each alien must appear at the tree only once).
For example, if d = 2, and beta-version of the family tree looks like this:
then Peter should add at least two ancestors to make it look well-formed:
Let Peter’s ancestors, appeared in the beta-version of his family tree, have identifiers from 1 to n (let Peter’s identifier be 0).
The first line of input file contains numbers n and d (2 ≤ n ≤ 100 000, 2 ≤ d ≤ n). The following line contains n numbers, the i-th number is an identifier of the child of the i-th alien.
Write the minimal number of Peter’s ancestors, that should be added to this tree to make it look well-formed.
6 2 5 5 0 5 0 5
Northeastern Europe 2006, Northern Subregion
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