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.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 10⁵) — 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.

Output

In a single line print n space-separated integers — c₁, c₂, ..., c_n.

Little Elephant and Tree

Examples