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E. Little Elephant and Tree

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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* ≤ 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.

Output

In a single line print *n* space-separated integers — *c*_{1}, *c*_{2}, ..., *c*_{n}.

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

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