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Contest: Task: Related: TaskC TaskE

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 $a = (1,1,2,1,1,2,2,4)$.