## QTREE3 - Query on a tree again!

 English Vietnamese

You are given a tree (an acyclic undirected connected graph) with N nodes. The tree nodes are numbered from 1 to N. In the start, the color of any node in the tree is white.

We will ask you to perfrom some instructions of the following form:

• 0 i : change the color of the i-th node (from white to black, or from black to white);
or
• 1 v : ask for the id of the first black node on the path from node 1 to node v. if it doesn't exist, you may return -1 as its result.

### Input

In the first line there are two integers N and Q.

In the next N-1 lines describe the edges in the tree: a line with two integers a b denotes an edge between a and b.

The next Q lines contain instructions "0 i" or "1 v" (1 ≤ i, v ≤ N).

### Output

For each "1 v" operation, write one integer representing its result.

### Example

```Input:
9 8
1 2
1 3
2 4
2 9
5 9
7 9
8 9
6 8
1 3
0 8
1 6
1 7
0 2
1 9
0 2
1 9

Output:
-1
8
-1
2
-1
```

### Constraints & Limits

There are 12 real input files.

For 1/3 of the test cases, N=5000, Q=400000.

For 1/3 of the test cases, N=10000, Q=300000.

For 1/3 of the test cases, N=100000, Q=100000.