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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php

// Scan N and M
fscanf(STDIN, "%d %d", $n, $m);
foreach (range(1, $n) as $j) {
    $acs[$j] = [];
}

$root = 0;
foreach (range(1, $n - 1 + $m) as $i) {
    fscanf(STDIN, "%d %d", $a, $b);
    $des[$a][$b] = 1;
    $acs[$b][$a] = 1;
    $root = empty($acs[$a]) ? $a : $root;
}
// print_array($acs);
// print_array($des);
detect_not_child($des, $acs, $root);

function detect_not_child(&$des, &$acs, $par)
{
    if (!isset($des[$par])) return;
    foreach (array_keys($des[$par]) as $child) {
        if ($acs[$child] !== [$par => 1]) {
            unset($acs[$child][$par]);
        }
    }
    foreach (array_keys($des[$par]) as $child) {
        detect_not_child($des, $acs, $child);
    }

}

print_ans($acs);

function print_ans($arr)
{
    foreach ($arr as $ar) {
        if (empty($ar)) echo "0\n";
        foreach ($ar as $k => $v) {
            echo $k . "\n";
        }
    }
}

function print_arrays(...$arrs)
{
    foreach ($arrs as $arr) {
        print_array($arr);
    }
}
function print_array($arr)
{
    if (empty($arr)) {
        echo "0";
    }
    foreach ($arr as $k => $e) {
        if (is_array($e)) {
            echo "$k ";
            print_array($e);
        } else {
            echo "$k ";
        }
    }
    echo "\n";
}