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)

DBG = !true
n,m = gets.split.map{|z| z.to_i}
child = Array.new(n)
child.map!{[]}
parent = Array.new(n)
parent.map!{[]}
for i in 0...(n-1+m)
  #a,b = gets.split.map{|z| z.to_i}
  a,b = gets.split
  a = a.to_i - 1
  b = b.to_i - 1
  child[a] << b
  parent[b] << a
end
print parent if DBG

height = Array.new(n,-1)
height_done = Array.new(n,false)
proc = []
for i in 0...n
  if child[i].size == 0
    proc << i
    height[i] = 0
  end
end

while !proc.empty?
  i = proc.shift
  for j in parent[i]
    proc << j #if !height_done[j]
    height_done[j] = true
    height[j] = height[i] + 1 if height[j] < height[i] + 1
  end
end

ht_suf = []
for i in 0...n
  ht_suf << [i, height[i]]
end
ht_suf.sort_by!{|z| z[1]}

realParent = Array.new(n,-1)
for i in 0...n
  j = ht_suf[i][0]
  if parent[j].size == 1
    realParent[j] = parent[j][0]
  elsif parent[j].size > 1
    mnht = 9999999
    mnsuf = -1
    for p in parent[j]
      if height[p] < mnht
        mnht = height[p]
        mnsuf = p
      end
    end
    realParent[j] = mnsuf
  end
  # do nothing if parent.sz == 0 i.e. root -> -1
end

for i in 0...n
  puts "#{realParent[i]+1}"
end