You are given a tree consising of N vertices. What is the minimum number of vertices that should be removed that all the remaining parts of the initial tree will contain less than K vertices?

Input
The first line contains one integer K. The second line contains one integer N. The third line contains N-1 space-separated intgers a_i for 2 <= i <= N which means that vertices i and a_i are connected by an edge.

Output
Output one number - answer for the question.

Constraints

• 1 <= K, N <= 10 000
• a_i < i