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.