For a tree with $n$ vertices, each vertex can be either white or black, initially all vertices are white. There are $q$ queries, each falling into one of two forms:
- `1 u`: All vertices on the path from the root to $u$ will become black.
- `2 u`: All vertices in the subtree rooted at $u$ will become white.
For each query, determine the number of vertices that change color after the query is executed.
### Input
- The first line consists of two integers $n,q$.
- The next $n - 1$ lines, each containing two integers $u,v$, indicating an edge between $u$ and $v$.
- The next $q$ lines, each representing a query in the specified format.
### Output
- After each query, print the number of vertices that change color.
### Constraints
- $1 \le n,q \le 10^5$.
- $1 \le u,v \le n$.
### Sample test
Input
```
6 4
1 2
1 3
3 4
3 5
2 6
1 2
2 3
1 4
2 3
```
Output:
```
2
0
2
2
```
