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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
#if DEBUG
            ReadLine();
#endif
        }

        public class Node
        {
            public int id;
            public List<int> parents;
            public List<int> children;
            public int level { get; set; }

            public Node(int id)
            {
                this.id = id;
                this.parents = new List<int>();
                this.children = new List<int>();
                this.level = -1;
            }
        }



        void Solve(ConsoleInput cin)
        {
            int n = cin.ReadInt;
            int m = cin.ReadInt;
            List<Node> graph = new List<Node>();

            for (int i = 0; i < n; i++)
            {
                graph.Add(new Node(i));
            }

            for (int i = 0; i < n - 1 + m; i++)
            {
                int a = cin.ReadInt - 1;
                int b = cin.ReadInt - 1;

                graph[a].children.Add(b);
                graph[b].parents.Add(a);
            }

            // 親を見つける
            int idParent = 0;
            while (graph[idParent].parents.Count() > 0)
            {
                idParent = graph[idParent].parents[0];
            }

            graph[idParent].level = 0;
            Queue<int> queue = new Queue<int>();
            queue.Enqueue(idParent);

            while (queue.Count() > 0)
            {
                int id = queue.Dequeue();

                foreach (int child in graph[id].children)
                {
                    if (graph[child].level == -1)
                    {
                        graph[child].level = graph[id].level + 1;
                        queue.Enqueue(child);
                    }
                    else if (graph[id].level + 1 > graph[child].level)
                    {
                        graph[child].level = graph[id].level + 1;
                        queue.Enqueue(child);
                    }
                    else
                    {
                        continue;
                    }
                }
            }

            for (int i = 0; i < n; i++)
            {
                if (graph[i].level == 0)
                {
                    Console.WriteLine("0");
                }
                else
                {
                    foreach (int parent in graph[i].parents)
                    {
                        if (graph[i].level - 1 == graph[parent].level)
                        {
                            Console.WriteLine(graph[parent].id + 1);
                            break;
                        }
                    }
                }
            }
        }

        class ConsoleInput
        {
            private readonly System.IO.TextReader _stream;
            private char _separator = ' ';
            private Queue<string> inputStream;

            public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
            {
                this._separator = separator;
                this._stream = stream;
                inputStream = new Queue<string>();
            }

            public string Read
            {
                get
                {
                    if (inputStream.Count != 0) return inputStream.Dequeue();
                    string[] tmp = _stream.ReadLine().Split(_separator);
                    for (int i = 0; i < tmp.Length; ++i)
                        inputStream.Enqueue(tmp[i]);
                    return inputStream.Dequeue();
                }
            }

            public string ReadLine { get { return _stream.ReadLine(); } }
            public int ReadInt { get { return int.Parse(Read); } }
            public long ReadLong { get { return long.Parse(Read); } }
            public double ReadDouble { get { return double.Parse(Read); } }
            public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
            public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
            public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        }
    }
}