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: Accepted)

N, M = gets.split.map(&:to_i)
edge_list = (N - 1 + M).times.map { gets.split.map(&:to_i) }
graph = Array.new(N) { [] }
indegree = Array.new(N) { 0 }
edge_list.each do |(u, v)|
  u -= 1; v -= 1
  graph[u].push(v)
  indegree[v] += 1
end

sorted = []
queue = []
indegree.each.with_index do |c, v|
  queue.push(v) if c == 0
end
while !queue.empty?
  v = queue.shift
  (graph[v]).each do |v2|
    indegree[v2] -= 1
    if indegree[v2] == 0
      queue.push(v2)
      sorted.push(v)
    end
  end
end

v_to_order = sorted.map.with_index { |v, i| [v, i] }.to_h
ans = Array.new(N) { sorted[0] }
ans[sorted[0]] = 0
edge_list.each do |(u, v)|
  u -= 1
  v -= 1
  ans[v] = u if v_to_order[u] > v_to_order[ans[v]]
end
ans.each.with_index do |v, i|
  if i == sorted[0]
    puts 0
  else
    puts(v + 1)
  end
end