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: Accepted)

import java.util.Scanner;
import java.util.ArrayList;
import java.util.LinkedList;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		int[] dg=new int[n];
		ArrayList<Integer>[] list=new ArrayList[n];
		for(int i=0; i<n; i++){
			list[i]=new ArrayList<>();
		}
		for(int i=0; i<n+m-1; i++){
			int a =sc.nextInt()-1;
			int b =sc.nextInt()-1;
			dg[b]++;
			list[a].add(b);
		}
		int root=0;
		for(int i=0; i<n; i++){
			if(dg[i]==0){
				root=i;
				break;
			}
		}
		int[] ans=new int[n];
		LinkedList<Integer> que=new LinkedList<>();
		que.add(root);
		while(!que.isEmpty()){
			int g=que.poll();
			for(int i:list[g]){
				dg[i]--;
				if(dg[i]==0){
					ans[i]=g+1;
					que.add(i);
				}
			}
		}
		for(int i=0; i<n; i++){
			System.out.println(ans[i]);
		}
	}
}