A9081. Xenia and Tree

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.

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.

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