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)

N, M = gets.strip.split(/ /).collect{|n| n.to_i}

$branches = {}
$branches_r = {}
(N - 1 + M).times{
	a, b = gets.strip.split(/ /).collect{|n| n.to_i}
	if l = $branches[a]
		l << b
	else
		$branches[a] = [b]
	end
	if l = $branches_r[b]
		l << a
	else
		$branches_r[b] = [a]
	end
}

def find_root
	n = 1
	while l = $branches_r[n]
		n = l[0]
	end
	n
end

def calc_distances(root)
	queue = [root]
	done = {}
	distances = []
	distances[root] = 0
	while n = queue.shift
		if l = $branches[n]
			d = distances[n] + 1
			l.each{|n2|
				if (d2 = distances[n2]) == nil || d > d2
					distances[n2] = d
					queue << n2
				end
			}
		end
	end
	distances
end

root = find_root
distances = calc_distances(root)

(1..N).each{|i|
	d = distances[i]
	if d == 0
		puts 0
	else
		puts $branches_r[i].collect{|x| [distances[x], x]}.max[1]
	end
}