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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int M = int.Parse(str[1]);
		int[][]A = new int[N+M-1][];
		for(var i=0;i<N+M-1;i++){
			string[] str2 = Console.ReadLine().Split();
			A[i] = new int[2]{int.Parse(str2[0]),int.Parse(str2[1])};
		}
		var list = new HashSet<int>[N];
		var list2 = new HashSet<int>[N];
		for(var i=0;i<N;i++){
			list[i] = new HashSet<int>();
			list2[i] = new HashSet<int>();
		}
		for(var i=0;i<N+M-1;i++){
			list[A[i][0]-1].Add(A[i][1]-1);
			list2[A[i][1]-1].Add(A[i][0]-1);
		}
		int[]C1 = new int[N];
		int[]C2 = new int[N];
		for(var i=0;i<N+M-1;i++){
			C1[A[i][0]-1]++;
			C2[A[i][1]-1]++;
		}
		int D1 = -1;
		for(var i=0;i<N;i++){
			if(list2[i].Count==0){
				D1 = i;
				break;
			}
		}
		int[]ans = new int[N];
		ans[D1] = 0;
		int ct = 1;
		int[]Lct = new int[N];
		int[]Nct = new int[N];
		for(var i=0;i<N;i++){
			Nct[i] = list2[i].Count;
		}
		while(ct<N){
          	int d2 = D1;
			foreach(var hs in list[D1]){
				Lct[hs]++;
				if(Nct[hs]==Lct[hs]){
					ans[hs] = D1+1;
					d2 = hs;
					ct++;
				}
			}
          	D1 = d2;
		}
		for(var i=0;i<N;i++){
			Console.WriteLine(ans[i]);
		}
	}
}