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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

$ii = 0;
while(<STDIN>){
	chomp;
	if ($_ =~ /.+/) {
    	if ($ii == 0) {
        	$N = [split(/ /, $_)]->[0];
        	$M = [split(/ /, $_)]->[1];
        } else {
        	@line = split(/ /, $_);
            $data[$ii-1][0] = $line[0];
            $data[$ii-1][1] = $line[1];
        }
        $ii++;
    }
}

$Ans = 0;
for ($node = 1; $node <= $N; $node++) {
	$tree[$node][0] = 0;	# Generation
	$tree[$node][1] = 0;	# Parent
}

for ($gen = 0; $gen < $N; $gen++) {
    for ($node = 1; $node <= $N; $node++) {
        if ( $tree[$node][0] == $gen ) {
            for ($ii = 0; $ii <= $#data; $ii++) {
            	if ($node == $data[$ii][1]) {
	            	if ($gen <= $tree[$data[$ii][0]][0]) {
                        $tree[$node][0] = $gen + 1;
                        $tree[$node][1] = $data[$ii][0];
	                }
                }
            }
        }
    }
}

for ($node = 1; $node <= $N; $node++) {
    #print "$node $tree[$node][0] $tree[$node][1]\n";
    print "$tree[$node][1]\n";
}