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Description

给定一颗n个结点的树，初始1号点为红色，其余点为蓝色。需要你设计数据结构实现两种功能。

1.将某个点涂为红色（若已为红色则无需更改）。

2.对于一个给出的点，输出从（此点）到（距离此点最近的红色点）的距离。

Input

第一行两个数n，m。代表树有n个结点，操作有m个。

接下来n - 1行，每行两个数u,v。代表这个树的边，其中u是根。

接下来m行，每行两个数，op，x

若op == 1，则将x涂红。

若op == 2，则输出从x到（距离x最近的红色点）的距离。

Output

对于每个op == 2，一行一个数表示答案。

Samples

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

0
3
2

Constraints

N = M = 100000

op = 1 or 2

1 <= x <= N

Note

It seems that our oj paodebisheidoukuai.If you passed this prob by brute force,but your solution which will be sent to us is not efficient enough,you wouldn't get this score.

Resources

2019 UESTC ACM Training for Data Structures