Spread of Information

AtCoder

IDarc116_e

Time3000ms

Memory256MB

Difficulty—

Takahashi Kingdom has $N$ towns, called Town $1$ through $N$. There are $N-1$ roads in this kingdom. The $i$\-th road connects Town $u_i$ and Town $v_i$ bidirectionally. For any two towns $a$ and $b$, it is possible to get from Town $a$ to Town $b$ by traversing some roads. Takahashi, the king, wants to spread some information all over the kingdom. Since he is busy, he can directly transmit this information to at most $K$ towns. Assume that Takahashi finishes transmitting the information at time $0$. Then, for each $t = 1, 2, 3, \cdots$, the following happens: * For towns $a$ and $b$ directly connected by a road, if $a$ has already received the information at time $t - 0.5$ but $b$ has not, $b$ receives it at time $t$. Takahashi wants to choose the $K$ towns to transmit the information to minimize the time taken until every town receives it. Find the minimum time this takes. ## Constraints * All values in input are integers. * $1 \leq K < N \leq 2 \times 10^5$ * $1 \leq u_i, v_i \leq N$ * For any two towns $a$ and $b$, it is possible to get from Town $a$ to Town $b$ by traversing some roads. ## Input Input is given from Standard Input in the following format: $N$ $K$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_{N-1}$ $v_{N-1}$ [samples]

Samples

Input #1

Output #1

1

If Takahashi directly transmits the information to Town $2$ and $4$, Town $1, 2, 3, 4, 5$ receives it at time $1, 0, 1, 0, 1$, respectively. In this case, the information is spread all over the kingdom at time $1$. We can prove that this is the earliest possible time.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Spread of Information",
    "description": {
      "content": "Takahashi Kingdom has $N$ towns, called Town $1$ through $N$. There are $N-1$ roads in this kingdom. The $i$\\-th road connects Town $u_i$ and Town $v_i$ bidirectionally. For any two towns $a$ and $b$,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc116_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi Kingdom has $N$ towns, called Town $1$ through $N$. There are $N-1$ roads in this kingdom. The $i$\\-th road connects Town $u_i$ and Town $v_i$ bidirectionally. For any two towns $a$ and $b$,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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