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.util.List;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Denis Nedelyaev
 */
public class Main {
    public static void main(String[] args) throws Exception {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        AtD solver = new AtD(in, out);
        solver.solve(1);
        out.close();
    }

    static class AtD {
        private final FastScanner in;
        private final PrintWriter out;
        private List<Integer>[] children;
        private int maxHeight;
        private int[] depth;
        private int[] parent;

        public AtD(FastScanner in, PrintWriter out) {
            this.in = in;
            this.out = out;
        }

        public void solve(int testNumber) throws InterruptedException {
            int n = in.nextInt();
            maxHeight = in.nextInt();
            parent = new int[n];

            for (int i = 0; i < n; i++) {
                parent[i] = in.nextInt() - 1;
            }

            children = new List[n];
            for (int i = 0; i < n; i++) {
                children[i] = new ArrayList<>();
            }
            for (int i = 1; i < n; i++) {
                children[parent[i]].add(i);
            }

            depth = new int[n];

            Thread thread = new Thread(null, this::solve, "solution", 1 << 24);
            thread.setUncaughtExceptionHandler((t, e) -> {
                throw new RuntimeException(e);
            });
            thread.start();
            thread.join();
        }

        private void solve() {
            calcDepth(0);
            out.println((parent[0] == 0 ? 0 : 1) + calc(0));
        }

        private int calcDepth(int v) {
            int ans = 0;
            for (int u : children[v]) {
                ans = Math.max(ans, calcDepth(u));
            }

            return depth[v] = (ans + 1) % maxHeight == 0 ? 0 : 1 + ans;
        }

        private int calc(int v) {
            int ans = 0;

            if (v != 0 && parent[v] != 0 && depth[v] == 0) {
                ans++;
            }

            for (int u : children[v]) {
                ans += calc(u);
            }

            return ans;
        }

    }

    static class FastScanner {
        private final InputStream in;
        private byte[] buffer = new byte[4096];
        private int pos = 0;
        private int size;

        public FastScanner(InputStream inputStream) throws IOException {
            in = inputStream;
            size = 0;
        }

        public int nextInt() {
            int c = skipWhitespace();

            int ans = 0;

            while (c > ' ') {
                ans *= 10;
                ans += c - '0';
                c = nextChar();
            }

            return ans;
        }

        private int skipWhitespace() {
            while (true) {
                int c = nextChar();
                if (c > ' ' || c == -1) {
                    return c;
                }
            }
        }

        private int nextChar() {
            if (pos >= size) {
                try {
                    size = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException("IO error");
                }
                if (size <= 0) {
                    return -1;
                }
                pos = 0;
            }
            return buffer[pos++];
        }

    }
}