Tree Queries

一棵树有 $n$ 个节点，初始均为白色，有两种操作： $1.$ $1\ x$ 代表把结点 $x$ 设置为黑色 $2.$ $2\ x$ 代表查询 $x$ 到树上任意一个黑色结点的简单路径上的编号最小的结点的编号 输入 $t$ 和 $z$ ，其中 $t$ 表示操作类型， $x=(last+z)mod\ n +1$，$last$代表上一次询问答案，初始为 $0$ ，保证第一个操作为 $1$

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}&lt;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.

4 6
1 2
2 3
3 4
1 2
1 2
2 2
1 3
2 2
2 2

3
2
1