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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;
using static System.Console;
using static System.Math;
class Z { static void Main() => new K(); }
class K
{
	int F => int.Parse(Str);
	long FL => long.Parse(Str);
	int[] G => Strs.Select(int.Parse).ToArray();
	long[] GL => Strs.Select(long.Parse).ToArray();
	string Str => ReadLine();
	string[] Strs => Str.Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries);
	const int MOD = 1000000007;
	public K()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		Solve();
		Out.Flush();
	}
	int V;
	Pair[] es;
	void Solve()
	{
		var I = G;
		V = I[0]; var E = I[1] + V - 1;
		es = new Pair[E];
		for (var e = 0; e < E; e++) { I = G; es[e] = new Pair(I[0] - 1, I[1] - 1); }
		TopologicalSort();
		var rev = new Dictionary<int, int>();
		for (var i = 0; i < V; i++) rev[topo[i]] = i;
		var par = new int[V];
		for (var i = 0; i < V; i++) par[i] = -1;
		foreach (var e in es) par[e.Y] = Max(par[e.Y], rev[e.X]);
		for (var i = 0; i < V; i++) WriteLine(par[i] < 0 ? 0 : topo[par[i]] + 1);
	}
	List<int> topo = new List<int>();
	void TopologicalSort()
	{
		topo.Clear();
		var s = new Queue<int>();
		var g = new List<int>[V];
		var rg = new int[V];
		for (var i = 0; i < V; i++) g[i] = new List<int>();
		foreach (var e in es) { g[e.X].Add(e.Y); rg[e.Y]++; }
		for (var i = 0; i < V; i++) if (rg[i] == 0) s.Enqueue(i);
		while (s.Count > 0)
		{
			var n = s.Dequeue();
			topo.Add(n);
			foreach (var m in g[n]) if (--rg[m] == 0) s.Enqueue(m);
		}
	}
}
struct Pair
{
	public readonly int X, Y;
	public Pair(int x, int y) { X = x; Y = y; }
}