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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
function tsort(e::Array{Int,2},n,m)
	g = [Int[] for i in 1:n]
	d = zeros(Int,n)
	v = zeros(Int,n)
	for i in 1:m
		push!(g[e[1,i]],e[2,i])
		d[e[2,i]] += 1
	end
	s = Int[]
	for i in 1:n
		if d[i] == 0
			push!(s,i)
		end
	end
	l = Int[]
	while !isempty(s)
		t = pop!(s)
		push!(l,t)
		for i in 1:length(g[t])
			d[g[t][i]] -= 1
			if d[g[t][i]] == 0
				push!(s,g[t][i])
			end
		end
	end
	if length(l) == n
		l
	else
		false
	end
end

function main()
	n,m = readline() |> split |> parseMap
	e = zeros(Int,2,n-1+m)
	g = [Int[] for i in 1:n]
	for i in 1:n-1+m
		e[:,i] = readline() |> split |> parseMap
		push!(g[e[2,i]],e[1,i])
	end
	ts = tsort(e,n,n+m-1)
	nm = zeros(Int,n)
	for i in 1:n
		nm[ts[i]] = i
	end
	t = zeros(Int,n)
	for i in n:-1:1
		mx = 0
		mi = 0
		for j in g[ts[i]]
			if nm[j]>mx
				mx = nm[j]
				mi = j
			end
		end
		t[ts[i]]=mi
	end
	for i in 1:n
		println(t[i])
	end
end

main()