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.