Contest Duration: - (local time) (110 minutes) Back to Home
D - Teleporter /

Time Limit: 1 sec / Memory Limit: 256 MB

### 問題文

それぞれの町にはテレポーターが 1 台ずつ設置されています。 町 i (1≤i≤N) のテレポーターの転送先は町 a_i (1≤a_i≤N) です。 どの町から出発しても、テレポーターを何回か使うことで首都へ辿り着けることが保証されます。

• どの町から出発しても、テレポーターをちょうど K 回使うと、最終的に首都にいる。

### 制約

• 2≤N≤10^5
• 1≤a_i≤N
• どの町から出発しても、テレポーターを何回か使うことで首都へ辿り着ける。
• 1≤K≤10^9

### 入力

N K
a_1 a_2 ... a_N


### 入力例 1

3 1
2 3 1


### 出力例 1

2


テレポーターの転送先を a = (1，1，1) と変えればよいです。

### 入力例 2

4 2
1 1 2 2


### 出力例 2

0


### 入力例 3

8 2
4 1 2 3 1 2 3 4


### 出力例 3

3


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).