There are N towns in Snuke Kingdom, conveniently numbered 1 through N. Town 1 is the capital.

Each town in the kingdom has a Teleporter, a facility that instantly transports a person to another place. The destination of the Teleporter of town i is town a_i (1≤a_i≤N). It is guaranteed that one can get to the capital from any town by using the Teleporters some number of times.

King Snuke loves the integer K. The selfish king wants to change the destination of the Teleporters so that the following holds:

* Starting from any town, one will be at the capital after using the Teleporters exactly K times in total.



Find the minimum number of the Teleporters whose destinations need to be changed in order to satisfy the king's desire.

Constraints

* 2≤N≤10^5
* 1≤a_i≤N
* One can get to the capital from any town by using the Teleporters some number of times.
* 1≤K≤10^9

Input

The input is given from Standard Input in the following format:


N K
a_1 a_2 ... a_N


Output

Print the minimum number of the Teleporters whose destinations need to be changed in order to satisfy King Snuke's desire.

Examples

Input

3 1
2 3 1


Output

2


Input

4 2
1 1 2 2


Output

0


Input

8 2
4 1 2 3 1 2 3 4


Output

3

public class Main {
  private static void solve() {
    int n = ni();
    int k = ni();
    
    int[] par = new int[n];
    for (int i = 0; i < n; i ++) {
      par[i] = ni() - 1;
    }
    int rootTo = par[0];
    par[0] = -1;
    int[][] g = parentToG(par);

    int[] ret = dfs(0, -1, g, k);
    
    int result = ret[1] + (rootTo != 0 ? 1 : 0);
    System.out.println(result);
    
  }

  private static int[] dfs(int now, int pre, int[][] g, int k) {
    int[] ret = {0, 0};
    for (int next : g[now]) {
      if (next == pre) continue;
      
      int[] v = dfs(next, now, g, k);
      ret[0] = Math.max(ret[0], v[0] + 1);
      ret[1] += v[1];
    }
    if (ret[0] == k - 1) {
      if (pre > 0) {
        ret[0] = -1;
        ret[1] ++;
      }
    }
    return ret;
  }
  
  public static int[][] parentToG(int[] par)
  {
      int n = par.length;
      int[] ct = new int[n];
      for(int i = 0;i < n;i++){
          if(par[i] >= 0){
              ct[i]++;
              ct[par[i]]++;
          }
      }
      int[][] g = new int[n][];
      for(int i = 0;i < n;i++){
          g[i] = new int[ct[i]];
      }
      for(int i = 0;i < n;i++){
          if(par[i] >= 0){
              g[par[i]][--ct[par[i]]] = i;
              g[i][--ct[i]] = par[i];
          }
      }
      return g;
  }
  
  
  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}
