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.util.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Main {
	private class Node {
		public int parentsCount = 0;
		public List<Integer> children = null;
		
		public int setParents = 0;
		public int trueParent = 0;
		public int trueDepth = 0;
		
		public Node() {
			children = new LinkedList<Integer>();
		}
		
		public void setDepth(int parent, int depth) {
			if (trueDepth < depth) {
				trueDepth = depth;
				trueParent = parent;
			}
			setParents++;
		}

		public int getDepth() {
			if (parentsCount > setParents) {
				return -1;
			}
			return trueDepth;
		}
		
		public int getTrueParent() {
			if (parentsCount > setParents) {
				return -1;
			}
			return trueParent;
		}
		
		public boolean isRoot() {
			if (parentsCount == 0) {
				return true;
			} else {
				return false;
			}
		}
	}
	
	private int getRoot(Node[] nodes) {
		int root = 0;
		for (root=1; root<nodes.length; root++) {
			if (nodes[root].isRoot()) {
				break;
			}
		}
		
		return root;
	}
	
	public void solve() {
		Scanner in = new Scanner(System.in);
		int N = in.nextInt();
		int M = in.nextInt();
		
		Node[] nodes = new Node[N+1];
		for (int i=0; i<N+1; i++) {
			nodes[i] = new Node();
		}
		
		for (int i=0; i<N+M-1; i++) {
			int a = in.nextInt();
			int b = in.nextInt();
			
			nodes[a].children.add(b);
			nodes[b].parentsCount++;
		}

		in.close();
		
		int root = getRoot(nodes);
		
		LinkedList<Integer> list = new LinkedList<Integer>();
		list.addFirst(root);
		
		while (list.size() > 0) {
			int target = list.removeFirst();
			int depth = nodes[target].getDepth();
			if (depth == -1) {
				// 別の親から入ってくるのを待つ
				continue;
			}
			
			for (Integer x : nodes[target].children) {
				nodes[x].setDepth(target, depth+1);
				list.addFirst(x);
			}
		}
		
		for (int i=1; i<N+1; i++) {
			System.out.println(nodes[i].getTrueParent());
		}
	}
	
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
	}
}