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)
es = (0..N).map{ [] }
rs = (0..N).map{ [] }
(N+M-1).times{
  a,b = gets.split.map(&:to_i)
  es[a] << b
  rs[b] << a
}

Root = (1..N).find{ |n| rs[n].size == 0 }

def topological_sort(node_num, edges, roots)
  ns = Array.new(node_num+1,0)
  edges.each{ |h| h.each{ |m| ns[m] += 1 } }
  nodes = roots.map{ |d| d }
  sorted = []
  while n = nodes.pop
    sorted << n
    edges[n].each{ |m|
      ns[m] -= 1
      if ns[m] == 0
        nodes << m
      end
    }
  end
  sorted
end

sorted = topological_sort(N, es, [Root])
dp = Array.new(N+1,0)
dp[sorted[0]] = 1
rs[Root] << 0
sorted.each{ |n|
  es[n].each{ |m|
    dp[m] = dp[n] + 1 if dp[n] >= dp[m]
  }
}
puts (1..N).map{ |m|
  rs[m].find{ |n| dp[m] == dp[n] + 1 }
}