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.util.*;
import java.util.stream.*;

class Main{
	static Scanner s=new Scanner(System.in);

	static class D{
		public D(int a,int b){
			this.a=a;
			this.b=b;
		}
		int a,b;
	}
	public static void main(String[] $){
		int n=s.nextInt(),m=s.nextInt();
		ArrayList<Set<Integer>>to=new ArrayList<>(n);
		ArrayList<Set<Integer>>from=new ArrayList<>(n);
		for(int i=0;i<n;++i) {
			to.add(new HashSet<>());
			from.add(new HashSet<>());
		}
		
		for(int e=n+m-1;e>0;--e) {
			int f=s.nextInt()-1;
			int t=s.nextInt()-1;
			to.get(f).add(t);
			from.get(t).add(f);
		}
		
		int root=IntStream.range(0,n).filter(i->from.get(i).isEmpty()).findAny().getAsInt();
		System.err.println(root);
		
		int[]parent=new int[n];
		
		ArrayDeque<Long>q=new ArrayDeque<>();
		for(int i:to.get(root)) {
			q.add((long)root*n+i);
		}
		while(!q.isEmpty()) {
			for(int _q=q.size();_q>0;--_q) {
				long p=q.poll();
				int pf=(int)p/n;
				int pt=(int)p%n;
				to.get(pf).remove(pt);
				from.get(pt).remove(pf);
				if(from.get(pt).isEmpty())
					parent[pt]=pf+1;
				
				for(int i:to.get(pt)) {
					q.add((long)pt*n+i);
				}
			}
		}
		Arrays.stream(parent).forEach(System.out::println);
	}
}