Problem:
Score : 500 points

Problem Statement

There is a rooted tree (see Notes) with N vertices numbered 1 to N.
Each of the vertices, except the root, has a directed edge coming from its parent.
Note that the root may not be Vertex 1.

Takahashi has added M new directed edges to this graph.
Each of these M edges, u \rightarrow v, extends from some vertex u to its descendant v.

You are given the directed graph with N vertices and N-1+M edges after Takahashi added edges.
More specifically, you are given N-1+M pairs of integers, (A_1, B_1), ..., (A_{N-1+M}, B_{N-1+M}), which represent that the i-th edge extends from Vertex A_i to Vertex B_i.

Restore the original rooted tree.

Notes

For "tree" and other related terms in graph theory, see the article in Wikipedia, for example.

Constraints

3 \leq N

1 \leq M

N + M \leq 10^5

1 \leq A_i, B_i \leq N

A_i \neq B_i

If i \neq j, (A_i, B_i) \neq (A_j, B_j).

The graph in input can be obtained by adding M edges satisfying the condition in the problem statement to a rooted tree with N vertices.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_{N-1+M} B_{N-1+M}

Output

Print N lines.
In the i-th line, print 0 if Vertex i is the root of the original tree, and otherwise print the integer representing the parent of Vertex i in the original tree.

Note that it can be shown that the original tree is uniquely determined.

Sample Input 1

3 1
1 2
1 3
2 3

Sample Output 1

0
1
2

The graph in this input is shown below:

It can be seen that this graph is obtained by adding the edge 1 \rightarrow 3 to the rooted tree 1 \rightarrow 2 \rightarrow 3.

Sample Input 2

6 3
2 1
2 3
4 1
4 2
6 1
2 6
4 6
6 5

Sample Output 2

6
4
2
0
6
2

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n, m = gets.split.map(&:to_i)
parents = {}
children = {}
(n + m - 1).times do |i|
  parent, child = gets.split.map(&:to_i)
  if parents[child]
    parents[child].push parent
  else
    parents[child] = [ parent ]
  end
  if children[parent]
    children[parent].push child
  else
    children[parent] = [ child ]
  end
end

root = nil
n.times do |i|
  tmp = i + 1
  unless parents[tmp]
    root = tmp
    break
  end
end
tmp_root = [ root ]

nodes = []
levels = { 0 => tmp_root }
level = 0
node_level_hash = {}
node_level_hash[root] = 0
while true
  nodes.concat levels[level]
  levels[level + 1] = []
  break_flg = true
  levels[level].each do |x|
    if children[x]
      children[x].each do |c|
        break_flg = false
        if parents[c].all?{|p| nodes.include?(p)}
          levels[level + 1].push c 
          node_level_hash[c] = level + 1
        end
      end
    end
  end
  break if break_flg
  level += 1
end

n.times do |i|
  tmp = i + 1
  if parents[tmp]
    puts "#{parents[tmp].find{ |p| node_level_hash[p] == (node_level_hash[tmp] - 1)}}"
  else
    puts "0"
  end
end