Code Submission Evaluation System Login

CSES Problem Set

Counting Paths


Task | Statistics


CSES - Counting Paths

Time limit:1.00 s Memory limit:512 MB

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

Your task is to calculate for each node the number of paths that contain the 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 that describe the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Finally, there are $m$ lines that describe 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 that contain the node.

Constraints
Example

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


Output:
3 1 3 1 1