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 \le i \le m) he first adds number i to lists of all nodes of a subtree with the root in node number ai, and then he adds number i to lists of all nodes of the subtree with root in node bi.

After applying all operations the Little Elephant wants to count for each node i number ci - the number of integers j (1 \le j \le n;j \neq 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 ci for him.

The first line contains two integers n and m (1 \le n,m \le 105) - the number of the tree nodes and the number of operations.

Each of the following n-1 lines contains two space-separated integers, ui and vi (1 \le ui,vi \le n,ui \neq vi), that mean that there is an edge between nodes number ui and vi.

Each of the following m lines contains two space-separated integers, ai and bi (1 \le ai,bi \le n,ai \neq bi), 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 - c1,c2,...,cn.