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: Runtime Error)

module N4
module_function
class UnionFind; def initialize(n); @p = *0...n; @r = [0] * n; end; def find(x); @p[x] == x ? x : @p[x] = find(@p[x]); end; def unite(x, y); x = find(x); y = find(y); return if x == y; if @r[x] < @r[y]; @p[x] = y; else; @p[y] = x; @r[x] += 1 if @r[x] == @r[y]; end; nil; end; def same(x, y); find(x) == find(y); end; end
end


(n,m),*ab=$<.map{|s|s.split.map &:to_i}

uf=N4::UnionFind.new(10**5+2)
par=$par=[]

def anc(a,b)
  $par[b]&&($par[b]==a||anc(a,$par[b]))
end

que=ab
until que.empty?
  a,b=que.shift
  if par[b]==nil
    par[b]=a
    uf.unite(a,b)
  elsif uf.same(a,b)
    if anc(par[b],a)
      par[b]=a
    end
  else
    que.push([a,b])
  end
end

puts par[1..-1].map{|e|e==nil ? 0 : e}