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 Kotlin (1.0.0) (judge verdict: Runtime Error)

import java.io.BufferedReader
import java.io.IOException
import java.io.InputStreamReader
import java.io.PrintWriter
import java.util.ArrayList
import java.util.StringTokenizer

class Main : Runnable {

    internal var ans: Int = 0
    internal var k: Int = 0
    internal var r: Array<MutableList<Int>>? = null

    internal fun dfs(q: Int, p: Int): Int {
        var h = 0
        for (w in r!![q]) {
            h = Math.max(h, dfs(w, q) + 1)
        }
        if (h == k - 1 && p != 0) {
            ans++
            h = -1
        }
        return h
    }

    @Throws(IOException::class)
    internal fun solve() {
        val n = nextInt()
        k = nextInt()
        r = Array(n) { ArrayList<Int>() }
        ans = 0
        for (i in 0..n - 1) {
            val q = nextInt()
            if (i != 0) r!![q - 1].add(i) else if (q != 1) ans++
        }
        dfs(0, 0)
        out.println(ans)
    }

    override fun run() {
        try {
            solve()
        } catch (e: Exception) {
            e.printStackTrace()
            System.exit(1)
        } finally {
            out.close()
        }
    }

    internal var `in` = BufferedReader(InputStreamReader(System.`in`))
    internal var out = PrintWriter(System.out)
    internal var st: StringTokenizer? = null

    @Throws(IOException::class)
    internal fun nextToken(): String {
        while (st == null || !st!!.hasMoreTokens()) st = StringTokenizer(`in`.readLine())
        return st!!.nextToken()
    }

    @Throws(IOException::class)
    internal fun nextInt(): Int {
        return Integer.parseInt(nextToken())
    }

    companion object {


        @JvmStatic fun main(args: Array<String>) {
            Thread(null, Main(), "name", (1 shl 27).toLong()).start()
        }
    }
}