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)

N,M=gets.split(" ").map(&:to_i)
A=Array.new(N+M-1,0),B=Array.new(N+M-1,0)
for i in 0..N+M-2
	ta,tb=gets.split(" ").map(&:to_i)
	A[i],B[i]=ta,tb
end
parent=Array.new(N+1).map{[]}
child=Array.new(N+1).map{[]}
for i in 0..N+M-2
	parent[B[i]].push(A[i])
	child[A[i]].push(B[i])
end

root=0
for i in 1..N
	size=parent[i].size
	if size==0
		root=i
	end
end

depth=Array.new(N+1,-1)

v=root
depth[v]=0
queue=[v]
checked=Array.new(N+1,0)
while !queue.empty?
	v=queue[0]
	child[v].each{|c|
		dep=depth[v]+1
		if depth[c]<dep
			depth[c]=dep
		end
		if checked[c]==0
			queue.push(c)
			checked[c]=1
		end
	}
	queue=queue.drop(1)
end
trueparent=Array.new(N+1,0)
for i in 0..N+M-2
	if depth[A[i]]+1==depth[B[i]]
		trueparent[B[i]]=A[i]
	end
end
puts trueparent[1..N]