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 x — change the color of vertex x to black. It is guaranteed that the first query will be of this type.
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.

Input

The first line contains two numbers n and q (3 ≤ n, q ≤ 10⁶).

Then n - 1 lines follow, each line containing two numbers x_i and y_i (1 ≤ x_i < 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 ith 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) mod n + 1.

It is guaranteed that the first query is of type 1, and there is at least one query of type 2.

Output

For each query of type 2 output the answer to it.

Tree Queries

Examples