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.io.BufferedOutputStream;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.SortedSet;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {

	static TreeMap<Integer, We> w = new TreeMap<>();
	static TreeSet<E> idx = new TreeSet<>();

	public static void main(String[] args) throws IOException {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		Set<Integer> from = new TreeSet<>();
		Set<Integer> to = new TreeSet<>();
		for (int i = 0; i < n - 1 + m; i++) {
			int a = in.nextInt();
			int b = in.nextInt();

			from.add(a);
			to.add(b);

			idx.add(new E(a, b));
		}

		from.removeAll(to);
		Integer root = from.iterator().next();
		hoge(root, 0, 0);

		BufferedOutputStream out = new BufferedOutputStream(System.out);
		OutputStreamWriter wri = new OutputStreamWriter(out);

		for (Map.Entry<Integer, We> e : w.entrySet()) {
			wri.write(String.valueOf(e.getValue().val) + "\n");
		}

		wri.flush();
		in.close();
	}

	public static void hoge(int root, int parent, int level) {
		w.merge(root, new We(level, parent), (old, v) -> {
			if (v.level > old.level) {
				return v;
			} else {
				return old;
			}
		});
		level++;
		SortedSet<E> set = idx.subSet(new E(root, -1), new E(root + 1, -1));
		if (set != null) {
			for (E e : set) {
				hoge(e.to, root, level);
			}
		}
	}

}

class We {
	int level;
	int val;
	public We(int level, int val) {
		this.level = level;
		this.val = val;
	}
}

@SuppressWarnings("rawtypes")
class E implements Comparable {
	int from;
	int to;
	public E(int from, int to) {
		this.from = from;
		this.to = to;
	}
	@Override
	public int compareTo(Object o) {
		int d = Integer.compare(this.from, ((E)o).from);
		if (d != 0) {
			return d;
		}
		return Integer.compare(this.to, ((E)o).to);
	}
	@Override
	public boolean equals(Object obj) {
		if (this == obj)
			return true;
		if (obj == null)
			return false;
		if (getClass() != obj.getClass())
			return false;
		E other = (E) obj;
		if (from != other.from)
			return false;
		if (to != other.to)
			return false;
		return true;
	}


}