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: Wrong Answer)

require 'tsort'

class Hash
  include TSort
  alias tsort_each_node each_key
  def tsort_each_child(node, &block)
    fetch(node).each(&block)
  end
end

def dfs(e,reve)
	stack = []
	reve.select{|k,v| v.size == 0}.each{|k,v|
		stack << k
	}
	# stack = reve.select{|a| a[1].size == 0}.to_a # not stack
	revnum = [0] + reve.map{|k,v| v.size} # incoming nodes numbers
	# p revnum
	# p stack
	result = []
	while(!stack.empty?)
		v = stack.pop
		result.push(v)
		# p "e #{e}"
		# p "v #{v}"
		# p "e[v] #{e[v]}"
		chs = e[v]
		chs.each{|ch|
			# p "ch #{ch}"
			# p "revnum[ch] #{revnum[ch]}"
			revnum[ch] -= 1
			# p "revnum[ch] reduced to #{revnum[ch]}"
			if(revnum[ch] == 0)
				result.push(ch)
				# p "children of #{ch} pushed"
				# p "#{e[ch]}"
				# p "stack #{stack}"
				stack += e[ch]
			end
		}
	end
	result
end

N,M=gets.split(" ").map{|i| i.to_i}
h = {}
revh = {} # child -> parents
for i in 0..(N-1)
	h[i+1] = []
	revh[i+1] = []
end
for i in 0..(N-2+M)
	a,b = gets.split(" ").map{|i| i.to_i}
	h[a].nil? ? h[a] = [b] : h[a] << b
	revh[b].nil? ? revh[b] = [a] : revh[b] << a
end
# p h
# p revh
tsort = dfs(h,revh)
# p tsort

node_level = Array.new(N+1) { |i| 0 }
parent = Array.new(N+1) { |i| 0 }
for i in 0..(N-1)
	node = tsort[i]
	h[node].each{|c|
		node_level[c] = node_level[node] + 1
		parent[c] = node
	}
end
# p node_level 
# p parent
for i in 1..(N)
	puts parent[i]
end