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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace _2019ni4
{
    class Program
    {
        class youso
        {
            public int PA;
            public int CH;
        }

        class tree
        {
            public tree P1;
            public tree P2;
            public int NUM;
            public int TP;
            public tree C1;
            public tree C2;
            public tree C3;
        }

        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int M = int.Parse(input[1]);
            List<youso> yo = new List<youso>();

            List<tree> tr = new List<tree>();

            for (int i = 0; i < N - 1 + M; i++)
            {
                youso tmp = new youso();
                string[] input2 = Console.ReadLine().Split(' ');
                tmp.PA = int.Parse(input2[0]);
                tmp.CH = int.Parse(input2[1]);

                yo.Add(tmp);

                tree tmp1, tmp2;

                tree result = tr.Find(fi => fi.NUM == yo[i].PA);
                if (result == null)
                {
                    tmp1 = new tree();
                    tmp1.NUM = yo[i].PA;
                    tr.Add(tmp1);
                }
                else
                {
                    tmp1 = result;
                }

                result = tr.Find(fi => fi.NUM == yo[i].CH);
                if (result == null)
                {
                    tmp2 = new tree();
                    tmp2.NUM = yo[i].CH;
                    tr.Add(tmp2);
                }
                else
                {
                    tmp2 = result;
                }

                if (tmp1.C1 == null)
                {
                    tmp1.C1 = tmp2;
                }
                else if (tmp1.C2 == null)
                {
                    tmp1.C2 = tmp2;
                }
                else
                {
                    tmp1.C3 = tmp2;
                }

                if (tmp2.P1 == null)
                {
                    tmp2.P1 = tmp1;
                }
                else
                {
                    tmp2.P2 = tmp1;
                }

            }

            tree ret = tr.Find(fi => fi.P1 == null);

            ret.TP = 1;

            treemake(ref ret);

            for(int i = 1; i <= N; i++)
            {
                int oya;
                tree tmp = tr.Find(fi => fi.NUM == i);

                if(tmp.P1 != null)
                {
                    if(tmp.P2 != null)
                    {
                        if (tmp.P1.TP > tmp.P2.TP)
                        {
                            oya = tmp.P1.NUM;
                        }
                        else
                        {
                            oya = tmp.P2.NUM;
                        }
                    }
                    else
                    {
                        oya = tmp.P1.NUM;
                    }
                }
                else
                {
                    oya = 0;

                }

                Console.WriteLine(oya);
            }
        }

        static void treemake(ref tree t1)
        {
            if(t1.C1 != null)
            {
                t1.C1.TP = t1.TP + 1;
                treemake(ref t1.C1);

            }
            if (t1.C2 != null)
            {
                t1.C2.TP = t1.TP + 1;
                treemake(ref t1.C2);
            }
            if (t1.C3 != null)
            {
                t1.C3.TP = t1.TP + 1;
                treemake(ref t1.C3);
            }


        }

    }
}