A8809. Little Elephant and Tree

The Little Elephant loves trees very much, he especially loves root trees.

He's got a tree consisting of $n$ nodes (the nodes are numbered from 1 to $n$ ), with root at node number $1$ . Each node of the tree contains some list of numbers which initially is empty.

The Little Elephant wants to apply $m$ operations. On the $i$ -th operation $(1<=i<=m)$ he first adds number $i$ to lists of all nodes of a subtree with the root in node number $a_{i}$ , and then he adds number $i$ to lists of all nodes of the subtree with root in node $b_{i}$ .

After applying all operations the Little Elephant wants to count for each node $i$ number $c_{i}$ — the number of integers $j$ $(1<=j<=n; j≠i)$ , such that the lists of the $i$ -th and the $j$ -th nodes contain at least one common number.

Help the Little Elephant, count numbers $c_{i}$ for him.

The first line contains two integers $n$ and $m$ $(1<=n,m<=10^{5})$ — the number of the tree nodes and the number of operations.

Each of the following $n-1$ lines contains two space-separated integers, $u_{i}$ and $v_{i}$ $(1<=u_{i},v_{i}<=n,u_{i}≠v_{i})$ , that mean that there is an edge between nodes number $u_{i}$ and $v_{i}$ .

Each of the following $m$ lines contains two space-separated integers, $a_{i}$ and $b_{i}$ $(1<=a_{i},b_{i}<=n,a_{i}≠b_{i})$ , that stand for the indexes of the nodes in the $i$ -th operation.

It is guaranteed that the given graph is an undirected tree.

In a single line print $n$ space-separated integers — $c_{1},c_{2},...,c_{n}$ .