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: Wrong Answer)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

class Node {
	int num;
	int parent = 0;
	int level = 0;
	List<Integer> childList = new ArrayList<Integer>();
}
public class Main {
	static List<Node> list = new ArrayList<Node>();

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		String line = in.nextLine();
		String[] split = line.trim().split("\\s+");
		int n = Integer.parseInt(split[0]);
		int m = Integer.parseInt(split[1]);
		for (int i = 1 ; i <= n ; i++) {
			Node node = new Node();
			node.num = i;
			list.add(node);
		}
		for (int i = 0 ; i < (n + m - 1) ; i++) {
			line = in.nextLine();
			split = line.trim().split("\\s+");
			int p = Integer.parseInt(split[0]);
			int c = Integer.parseInt(split[1]);
			list.get(p-1).childList.add(c);
			list.get(c-1).parent = -1;
		}
		in.close();

		Node rootNode = list.get(0);
		for (Node node : list) {
			if (node.parent == 0) {
				rootNode = node;
				break;
			}
		}

		retrieve(rootNode, 1);

		for (Node node : list) {
			System.out.println(node.parent);
		}
	}

	private static void retrieve(Node node, int level) {
		for (int i : node.childList) {
			Node child = list.get(i-1);
			if (child.level > level) break;
			child.parent = node.num;
			child.level = level;
			retrieve(child, level + 1);
		}
	}
}