# Counting Offspring

Time Limit: 15000/5000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

## Description

You are given a tree, it’s root is p, and the node is numbered from 1 to n. Now define f(i) as the number of nodes whose number is less than i in all the succeeding nodes of node i. Now we need to calculate f(i) for any possible i.

## Input

Multiple cases (no more than 10), for each case:
The first line contains two integers n (0<n<=10^5) and p, representing this tree has n nodes, its root is p.
Following n-1 lines, each line has two integers, representing an edge in this tree.
The input terminates with two zeros.

## Output

For each test case, output n integer in one line representing f(1), f(2) … f(n), separated by a space.

## Sample Input

15 7
7 10
7 1
7 9
7 3
7 4
10 14
14 2
14 13
9 11
9 6
6 5
6 8
3 15
3 12
0 0

## Sample Output

0 0 0 0 0 1 6 0 3 1 0 0 0 2 0

lcy

## Source

2011 Multi-University Training Contest 5 -