Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

3 1
2 3 1

Sample Output 1

2

Change the destinations of the Teleporters to a = (1,1,1).

Sample Input 2

4 2
1 1 2 2

Sample Output 2

0

There is no need to change the destinations of the Teleporters, since the king's desire is already satisfied.

Sample Input 3

8 2
4 1 2 3 1 2 3 4

Sample Output 3

3

For example, change the destinations of the Teleporters to a = (1,1,2,1,1,2,2,4).

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Niyaz Nigmatullin
 */
public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            @Override
            public void run() {
                InputStream inputStream = System.in;
                OutputStream outputStream = System.out;
                FastScanner in = new FastScanner(inputStream);
                FastPrinter out = new FastPrinter(outputStream);
                TaskD solver = new TaskD();
                solver.solve(1, in, out);
                out.close();

            }
        }, "", 1 << 27).start();
    }

    static class TaskD {
        static List<Integer>[] edges;
        static int[] kill;
        static int[] left;
        static int k;

        public void solve(int testNumber, FastScanner in, FastPrinter out) {
            int n = in.nextInt();
            k = in.nextInt();
            int[] a = in.readIntArray(n);
            for (int i = 0; i < n; i++) --a[i];
            int ans = 0;
            if (a[0] != 0) {
                a[0] = 0;
                ans++;
            }
            edges = new List[n];
            for (int i = 0; i < n; i++) {
                edges[i] = new ArrayList<>();
            }
            for (int i = 1; i < n; i++) {
                edges[a[i]].add(i);
            }
            kill = new int[n];
            left = new int[n];
            dfs(0);
            out.println(kill[0] + ans);
        }

        static void dfs(int v) {
            kill[v] = 0;
            left[v] = 0;
            for (int it = 0; it < edges[v].size(); it++) {
                int to = edges[v].get(it);
                dfs(to);
                kill[v] += kill[to];
                if (left[to] == k - 1 && v != 0) {
                    kill[v]++;
                } else {
                    left[v] = Math.max(left[v], left[to] + 1);
                }
            }
        }

    }

    static class FastScanner extends BufferedReader {
        public FastScanner(InputStream is) {
            super(new InputStreamReader(is));
        }


        public int read() {
            try {
                int ret = super.read();
//            if (isEOF && ret < 0) {
//                throw new InputMismatchException();
//            }
//            isEOF = ret == -1;
                return ret;
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }

        static boolean isWhiteSpace(int c) {
            return c >= 0 && c <= 32;
        }

        public int nextInt() {
            int c = read();
            while (isWhiteSpace(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int ret = 0;
            while (c >= 0 && !isWhiteSpace(c)) {
                if (c < '0' || c > '9') {
                    throw new NumberFormatException("digit expected " + (char) c
                            + " found");
                }
                ret = ret * 10 + c - '0';
                c = read();
            }
            return ret * sgn;
        }

        public String readLine() {
            try {
                return super.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public int[] readIntArray(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

    }

    static class FastPrinter extends PrintWriter {
        public FastPrinter(OutputStream out) {
            super(out);
        }

        public FastPrinter(Writer out) {
            super(out);
        }

    }
}