# Xenia and Tree

## 题目描述

Xenia the programmer has a tree consisting of \$ n \$ nodes. We will consider the tree nodes indexed from 1 to \$ n \$ . We will also consider the first node to be initially painted red, and the other nodes — to be painted blue. The distance between two tree nodes \$ v \$ and \$ u \$ is the number of edges in the shortest path between \$ v \$ and \$ u \$ . Xenia needs to learn how to quickly execute queries of two types: 1. paint a specified blue node in red; 2. calculate which red node is the closest to the given one and print the shortest distance to the closest red node. Your task is to write a program which will execute the described queries.

## 输入输出格式

### 输入格式

The first line contains two integers \$ n \$ and \$ m \$ \$ (2<=n<=10^{5},1<=m<=10^{5}) \$ — the number of nodes in the tree and the number of queries. Next \$ n-1 \$ lines contain the tree edges, the \$ i \$ -th line contains a pair of integers \$ a_{i},b_{i} \$ \$ (1<=a_{i},b_{i}<=n,a_{i}≠b_{i}) \$ — an edge of the tree. Next \$ m \$ lines contain queries. Each query is specified as a pair of integers \$ t_{i},v_{i} \$ \$ (1<=t_{i}<=2,1<=v_{i}<=n) \$ . If \$ t_{i}=1 \$ , then as a reply to the query we need to paint a blue node \$ v_{i} \$ in red. If \$ t_{i}=2 \$ , then we should reply to the query by printing the shortest distance from some red node to node \$ v_{i} \$ . It is guaranteed that the given graph is a tree and that all queries are correct.

### 输出格式

For each second type query print the reply in a single line.

## 输入输出样例

### 输入样例 #1

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

### 输出样例 #1

``````0
3
2
``````