D - Collision

Score : $400$ points

Problem Statement

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:

$N$ $Q$

$a_1$ $b_1$

$a_2$ $b_2$

$\hspace{0.6cm}\vdots$

$a_{N-1}$ $b_{N-1}$

$c_1$ $d_1$

$c_2$ $d_2$

$\hspace{0.6cm}\vdots$

$c_Q$ $d_Q$

Output

Print $Q$ lines. The $i$-th line $(1 \leq i \leq Q)$ should contain Town if Takahashi and Aoki will meet at a town in the $i$-th query, and Road if they meet halfway along a road in that query.

4 1
1 2
2 3
2 4
1 2

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.

5 2
1 2
2 3
3 4
4 5
1 3
1 5

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.

9 9
2 3
5 6
4 8
8 9
4 5
3 4
1 9
3 7
7 9
2 5
2 6
4 6
2 4
5 8
7 8
3 6
5 6

Town
Road
Town
Town
Town
Town
Road
Road
Road