Reminder: in case of any technical issues, you can use the lightweight website
m1.codeforces.com,
m2.codeforces.com,
m3.codeforces.com.
×

Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/08/2020 18:59:14 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|