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

Example Output

3 1 3 1 1