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: Accepted)


import java.util.*;
import java.util.concurrent.LinkedBlockingDeque;

public class Main {
    public static class Node {
        int current;
        int father;
        public Node(int current, int father) {
            this.current = current;
            this.father = father;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Node node = (Node) o;

            if (current != node.current) return false;
            return father == node.father;

        }

        @Override
        public int hashCode() {
            int result = current;
            result = 31 * result + father;
            return result;
        }
    }
    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        Map<Integer, Set<Integer>> fathers = new HashMap<>();
        Map<Integer, Set<Integer>> sons = new HashMap<>();
        Set<Integer> roots = new HashSet<>();
        int [] fatherCounts = new int[n + 1];
        for (int i = 1; i <= n; ++i) {
            roots.add(i);
        }
        for (int i = 0; i < n + m - 1; i++) {
            int u = scanner.nextInt();
            int v = scanner.nextInt();
            Set<Integer> descendants = sons.getOrDefault(u, new HashSet<>());
            descendants.add(v);
            sons.put(u, descendants);
            roots.remove(v);
            ++fatherCounts[v];
            Set<Integer> parents = fathers.getOrDefault(v, new HashSet<>());
            parents.add(u);
            fathers.put(v, parents);
        }
        int root = -1;
        for (final int r : roots) {
            root = r;
        }
        int [] reorder = new int[n];
        int numNode = 0;
        reorder[numNode++] = root;
        Map<Integer, Integer> nodeReorder = new HashMap<>();
        nodeReorder.put(root, 0);
        for (int i = 0; i < numNode; ++i) {
            for (int son : sons.getOrDefault(reorder[i], new HashSet<>())) {
                if (--fatherCounts[son] == 0) {
                    reorder[numNode++] = son;
                    nodeReorder.put(son, numNode - 1);
                }
            }
        }

        for (int i = 1; i <= n; ++i) {
            if (!fathers.containsKey(i)) {
                System.out.println(0);
                continue;
            }
            int fatherWithMaxReorder = -1;
            for (int father : fathers.get(i)) {
                if (fatherWithMaxReorder == -1 || nodeReorder.get(father) > nodeReorder.get(fatherWithMaxReorder)) {
                    fatherWithMaxReorder = father;
                }
            }

            System.out.println(fatherWithMaxReorder);
        }

    }
}