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: Accepted)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    /**
     * 整数K
     */
    private static int K;

    /**
     * ある町へ転送するテレポータが設置されている町のリスト
     */
    private static List<List<Integer>> vec = new ArrayList<>();

    /**
     * 転送先を変えなければならないテレポータの数
     */
    private static int ans = 0;

    public static void main(String args[]) {
        //スタックサイズ2^24で処理を行う
        new Thread(null, () -> {
            //try-with-resources文(カッコ内で宣言した変数はtry句を抜けると自動的に閉じられる)
            try (Scanner sc = new Scanner(System.in)) {
                int n = sc.nextInt();
                K = sc.nextInt();
                for (int i = 0; i < n; i++) {
                    vec.add(new ArrayList<>());
                }
                for (int i = 0; i < n; i++) {
                    int a = sc.nextInt() - 1;
                    if (i != 0) {
                        vec.get(a).add(i);
                    } else if (a != 0) {
                        ans++;
                    }
                }
            }

            dfs(0, 0);
            System.out.println(ans);
        }, "", 1 << 24).start();
    }

    /**
     * 転送回数を算出する
     *
     * @param v   着目する町
     * @param pre 1つ前の町
     * @return 転送回数
     */
    private static int dfs(int v, int pre) {
        int height = 0;

        //拡張for文(リストや配列から要素を1つずつ取り出す)
        for (int j : vec.get(v)) {
            height = Math.max(height, dfs(j, v));
        }

        if (pre != 0 && height == K - 1) {
            height = 0;
            ans++;
        } else {
            height++;
        }

        return height;
    }
}