Counting Paths

• Time limit: 1.00 s
• Memory limit: 512 MB

You are given a tree consisting of $n$ nodes, and $m$ paths in the tree.

Your task is to calculate for each node the number of paths containing that node.

Input

The first input line contains integers $n$ and $m$: the number of nodes and paths. The nodes are numbered $1,2,\ldots,n$.

Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Finally, there are $m$ lines describing the paths. Each line contains two integers $a$ and $b$: there is a path between nodes $a$ and $b$.

Output

Print $n$ integers: for each node $1,2,\ldots,n$, the number of paths containing that node.

Constraints

• $1 \le n, m \le 2 \cdot 10^5$
  
• $1 \le a,b \le n$
  

Example

Input:
5 3
1 2
1 3
3 4
3 5
1 3
2 5
1 4

Output:
3 1 3 1 1