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

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`