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.

输入描述:

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.

输出描述:

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