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:
paint a specified blue node in red;
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.
Input
The first line contains two integers n and m(2≤n≤105,1≤m≤105) − 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 ai,bi(1≤ai,bi≤n,ai≠bi) − an edge of the tree.
Next m lines contain queries. Each query is specified as a pair of integers ti,vi(1≤ti≤2,1≤vi≤n). If ti=1, then as a reply to the query we need to paint a blue node vi in red. If ti=2, then we should reply to the query by printing the shortest distance from some red node to node vi.
It is guaranteed that the given graph is a tree and that all queries are correct.
Output
For each second type query print the reply in a single line.