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.*;

public class Main {
	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();

		List<Integer>[] g = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			g[i] = new ArrayList<>();
		}

		for (int i = 0; i < n - 1 + m; i++) {
			g[sc.nextInt() - 1].add(sc.nextInt() - 1);
		}

		TopologicalSort ts = new TopologicalSort(g);

		int[] parents = new int[n];
		Iterable<Integer> order = ts.order();
		for (int i : order) {
			//System.out.print("S:  ");
			//System.out.println(i);
			for (int j = 0; j < g[i].size(); j++) {
				parents[g[i].get(j)] = i + 1;
			}
		}
		for (int i = 0; i < n; i++) {
			System.out.println(parents[i]);
		}
	}

	private static class TopologicalSort {
		List<Integer>[] g;
		Queue<Integer> q = new LinkedList<>();
		boolean visited[];

		public TopologicalSort(List<Integer>[] g) {
			this.g = g;
			visited = new boolean[g.length];

			for (int v = 0; v < g.length; v++) {
				if (!visited[v]) dfs(v);
			}
		}

		public Iterable<Integer> order() {
			Stack<Integer> reverse = new Stack<>();
			for (int i : q) {
				reverse.push(i);
			}
			List<Integer> a = new ArrayList();
			while (!reverse.isEmpty())
				a.add(reverse.pop());
			return a;
		}

		private void dfs(int v) {
			if (visited[v]) return;
			visited[v] = true;
			for (Integer i : g[v]) {
				dfs(i);
			}
			q.offer(v);
		}
	}
}