Teleporter

AtCoder

IDagc004_d

Time1000ms

Memory256MB

Difficulty—

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: $N$ $K$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

3 1
2 3 1

Output #1

2

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

Input #2

4 2
1 1 2 2

Output #2

0

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

Input #3

8 2
4 1 2 3 1 2 3 4

Output #3

3

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

API Response (JSON)

{
  "problem": {
    "name": "Teleporter",
    "description": {
      "content": "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 anot",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc004_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ towns in Snuke Kingdom, conveniently numbered $1$ through $N$. Town $1$ is the capital.\nEach town in the kingdom has a _Teleporter_, a facility that instantly transports a person to anot...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments