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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String[] nm = scanner.nextLine().split(" ", 2);
        int n = Integer.parseInt(nm[0]);
        int m = Integer.parseInt(nm[1]);

        Map<Integer, Integer> inputMap = new HashMap<>();
        Map<Integer, Set<Integer>> parentsMap = new HashMap<>();
        for (int i = 0; i < n - 1 + m; i++) {
            String[] ab = scanner.nextLine().split(" ", 2);
            int a = Integer.parseInt(ab[0]);
            int b = Integer.parseInt(ab[1]);
            inputMap.put(a, b);

            Set<Integer> parents = parentsMap.get(b);
            if (parents == null) {
                parents = new HashSet<>();
                parentsMap.put(b, parents);
            }
            parents.add(a);
        }

        //int root = 0;
        //for (int i = 1; i <= n; i++) {
        //    if (!parentsMap.containsKey(i)) {
        //        root = i;
        //        break;
        //    }
        //}

        // prepare indirect parents
        Map<Integer, Set<Integer>> indirectParentsMap = new HashMap<>();
        for (Map.Entry<Integer, Set<Integer>> entry : parentsMap.entrySet()) {
            Integer child = entry.getKey();
            for (Integer parent : entry.getValue()) {
                addParentParents(indirectParentsMap, parentsMap, child, parent);
            }
        }

        // detect unnecessary vector
        Map<Integer, Integer> parentMap = new HashMap<>();
        for (Map.Entry<Integer, Set<Integer>> entry : parentsMap.entrySet()) {
            Integer child = entry.getKey();
            Set<Integer> parents = entry.getValue();
            if (parents.size() == 1) {
                for (Integer parent : parents) {
                    parentMap.put(child, parent);
                }
                continue;
            }

            Set<Integer> indirectParents = indirectParentsMap.get(child);
            for (Integer parent : parents) {
                if (indirectParents.contains(parent)) {
                    // remove this path
                } else {
                    parentMap.put(child, parent);
                }
            }
        }

        for (int i = 1; i <= n; i++) {
            if (parentMap.containsKey(i)) {
                System.out.println(parentMap.get(i));
            } else {
                System.out.println(0);
            }
        }
    }

    private static void addParentParents(Map<Integer, Set<Integer>> indirectParentsMap,
            Map<Integer, Set<Integer>> parentsMap, Integer child, Integer parent) {
        Set<Integer> parentParents = parentsMap.get(parent);
        if (parentParents == null) {
            return;
        }

        Set<Integer> indirectParents = indirectParentsMap.get(child);
        if (indirectParents == null) {
            indirectParents = new HashSet<>();
            indirectParentsMap.put(child, indirectParents);
        }

        for (Integer parentParent : parentParents) {
            indirectParents.add(parentParent);
            addParentParents(indirectParentsMap, parentsMap, child, parentParent);
        }
    }
}