Collision

AtCoder

IDabc209_d

Time2000ms

Memory256MB

Difficulty—

The Kingdom of Takahashi is made up of $N$ towns and $N-1$ roads, where the towns are numbered $1$ through $N$. The $i$\-th road $(1 \leq i \leq N-1)$ connects Town $a_i$ and Town $b_i$, so that you can get from every town to every town by using some roads. **All the roads have the same length.** You will be given $Q$ queries. In the $i$\-th query $(1 \leq i \leq Q)$, given integers $c_i$ and $d_i$, solve the following problem: * Takahashi is now at Town $c_i$ and Aoki is now at Town $d_i$. They will leave the towns simultaneously and start traveling at the same speed, Takahashi heading to Town $d_i$ and Aoki heading to Town $c_i$. Determine whether they will meet at a town or halfway along a road. Here, assume that both of them travel along the shortest paths, and the time it takes to pass towns is negligible. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq Q \leq 10^5$ * $1 \leq a_i < b_i \leq N\, (1 \leq i \leq N-1)$ * $1 \leq c_i < d_i \leq N\, (1 \leq i \leq Q)$ * All values in input are integers. * It is possible to get from every town to every town by using some roads. ## Input Input is given from Standard Input in the following format: $N$ $Q$ $a_1$ $b_1$ $a_2$ $b_2$ $\hspace{0.6cm}\vdots$ $a_{N-1}$ $b_{N-1}$ $c_1$ $d_1$ $c_2$ $d_2$ $\hspace{0.6cm}\vdots$ $c_Q$ $d_Q$ [samples]

Samples

Input #1

Output #1

Road

In the first and only query, Takahashi and Aoki simultaneously leave Town $1$ and Town $2$, respectively, and they will meet halfway along the $1$\-st road, so we should print `Road`.

Input #2

Output #2

Town
Town

In the first query, Takahashi and Aoki simultaneously leave Town $1$ and Town $3$, respectively, and they will meet at Town $2$, so we should print `Town`.
In the first query, Takahashi and Aoki simultaneously leave Town $1$ and Town $5$, respectively, and they will meet at Town $3$, so we should print `Town`.

Input #3

Output #3

Town
Road
Town
Town
Town
Town
Road
Road
Road

API Response (JSON)

{
  "problem": {
    "name": "Collision",
    "description": {
      "content": "The Kingdom of Takahashi is made up of $N$ towns and $N-1$ roads, where the towns are numbered $1$ through $N$. The $i$\\-th road $(1 \\leq i \\leq N-1)$ connects Town $a_i$ and Town $b_i$, so that you c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc209_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The Kingdom of Takahashi is made up of $N$ towns and $N-1$ roads, where the towns are numbered $1$ through $N$. The $i$\\-th road $(1 \\leq i \\leq N-1)$ connects Town $a_i$ and Town $b_i$, so that you c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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