== include(page="template/taskheader" task_id="connectthetree") ==

Poveste şi cerinţă...

You are given a tree with $N$ nodes. You should process $M$ queries of two types:
 
$1$ $x$ $y$: (x, y) is an edge from the initial tree. If the edge (x, y) is still in the tree, delete it, else add it back.
 
$2$ $x$ $y$: this output is either $0$ or $1$. Consider that total is the sum of all the previous type 2 queries. Then compute $x_new$ = (x + total) mod $N$ + $1$, $y_new$ = (y + total) mod $N$ + $1$.
 
Output $1$ if you can reach $y_new$ from $x_new$, or $0$ if you cannot.

h2. Date de intrare

Fişierul de intrare $connectthetree.in$ ...

The first line of the input file $connectthetree.in$ will contain $N$, $M$.
 
On the next $N-1$ lines you will find the description of the tree. On each line there will be a pair ($x, y$), representing that there will be an edge between $x$ and $y$.
 
On the next $M$ lines you will find a triplet ($t, x, y$) representing a query, $t$ is $1$ or $2$.

h2. Date de ieşire

În fişierul de ieşire $connectthetree.out$ ...

The output file $connectthetree.out$ will contain as many lines as there are type $2$ queries in the input. The ith line will contain the answer for the ith type $2$ query.

h2. Restricţii

* $... ≤ ... ≤ ...$

* $2 ≤ N, M ≤ 2.5 * 10^5$
* For tests worth $25$ points, $1 ≤ N, M ≤ 1000$.
* For tests worth $15$ more points, $1 ≤ N ≤ 1000$.

h2. Exemplu
table(example). |_. connectthetree.in |_. connectthetree.out |

| This is some
  text written on
  multiple lines.
| This is another
  text written on
  multiple lines.

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

|

h3. Explicaţie
 
...

== include(page="template/taskfooter" task_id="connectthetree") ==