A10984. Tree Queries

You are given a tree consisting of $n$ vertices (numbered from $1$ to $n$ ). Initially all vertices are white. You have to process $q$ queries of two different types:

1. $1$ $x$ — change the color of vertex $x$ to black. It is guaranteed that the first query will be of this type.
2. $2$ $x$ — for the vertex $x$ , find the minimum index $y$ such that the vertex with index $y$ belongs to the simple path from $x$ to some black vertex (a simple path never visits any vertex more than once).

For each query of type $2$ print the answer to it.

Note that the queries are given in modified way.

The first line contains two numbers $n$ and $q$ ( $3<=n,q<=10^{6}$ ).

Then $n-1$ lines follow, each line containing two numbers $x_{i}$ and $y_{i}$ ( $1<=x_{i}<y_{i}<=n$ ) and representing the edge between vertices $x_{i}$ and $y_{i}$ .

It is guaranteed that these edges form a tree.

Then $q$ lines follow. Each line contains two integers $t_{i}$ and $z_{i}$ , where $t_{i}$ is the type of $i$ th query, and $z_{i}$ can be used to restore $x_{i}$ for this query in this way: you have to keep track of the answer to the last query of type $2$ (let's call this answer $last$ , and initially $last=0$ ); then $x_{i}=(z_{i}+last)modn+1$ .

It is guaranteed that the first query is of type $1$ , and there is at least one query of type $2$ .

For each query of type $2$ output the answer to it.