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 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 ≤ 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 ci 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, ui and vi (1 ≤ ui, vi ≤ n, ui ≠ 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 ≤ ai, bi ≤ n, ai ≠ 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.

Output

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

Examples

Input

5 1 1 2 1 3 3 5 3 4 2 3

Output

0 3 3 3 3

Input

11 3 1 2 2 3 2 4 1 5 5 6 5 7 5 8 6 9 8 10 8 11 2 9 3 6 2 8

Output

0 6 7 6 0 2 0 5 4 5 5

inputFormat

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, ui and vi (1 ≤ ui, vi ≤ n, ui ≠ 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 ≤ ai, bi ≤ n, ai ≠ 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.

outputFormat

Output

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

Examples

Input

5 1 1 2 1 3 3 5 3 4 2 3

Output

0 3 3 3 3

Input

11 3 1 2 2 3 2 4 1 5 5 6 5 7 5 8 6 9 8 10 8 11 2 9 3 6 2 8

Output

0 6 7 6 0 2 0 5 4 5 5

样例

5 1
1 2
1 3
3 5
3 4
2 3

0 3 3 3 3 

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