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.

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 $b$ .

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

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