Counting Paths

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