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 $a_i$ ($1 \leq a_i \leq N$). 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

• $2 \leq N \leq 10^5$
• $1 \leq a_i \leq N$
• One can get to the capital from any town by using the Teleporters some number of times.
• $1 \leq K \leq 10^9$

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.

3 1
2 3 1

2

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

4 2
1 1 2 2

0

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

8 2
4 1 2 3 1 2 3 4

3

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