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: Runtime Error)

import java.io.*;
import java.util.*;
import java.util.function.*;

final class Solver {
	static final Solver INSTANCE = new Solver();

	void solve(Supplier<String> sc) {
		int N = Integer.parseInt(sc.get());
		int M = Integer.parseInt(sc.get());
		BitSet[] graph = new BitSet[N];
		BitSet[] reversed = new BitSet[N];
		int root;
		{
			BitSet child = new BitSet(N);
			Arrays.setAll(graph, $ -> new BitSet(N));
			Arrays.setAll(reversed, $ -> new BitSet(N));
			for (int i = 0; i < N - 1 + M; i++) {
				int A = Integer.parseInt(sc.get()) - 1;
				int B = Integer.parseInt(sc.get()) - 1;

				graph[A].set(B);
				reversed[B].set(A);

				child.set(B);
			}
			root = child.nextClearBit(0);
		}

		Queue<Integer> queue = new ArrayDeque<>();
		queue.add(root);
		int[] parent = new int[N];
		while (!queue.isEmpty()) {
			int remove = queue.remove();
			for (int next = graph[remove].nextSetBit(0); next >= 0; next = graph[remove].nextSetBit(next)) {
				reversed[next].clear(remove);
				if (!reversed[next].isEmpty()) continue;
				parent[next] = remove;
				queue.add(next);
			}
		}
		parent[root] = -1;
		for (int i : parent) {
			System.out.println(i + 1);
		}
	}
}

class Main {
	public static void main(String... args) {
		System.setOut(new PrintStream(new BufferedOutputStream(System.out)));
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		Solver.INSTANCE.solve(new Supplier<String>() {
			StringTokenizer line;

			public String get() {
				try {
					return (line = line != null && line.hasMoreTokens() ? line : new StringTokenizer(reader.readLine())).nextToken();
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
		});
		System.out.flush();
	}
}