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.Linq;
using System.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N, _M, M;
        public Graph G;
        public void Run()
        {
            // Input
            {
                var line = Input.ReadIntArray();
                N = line[0];
                _M = line[1];
                M = N - 1 + _M;
            }

            // Graph
            G = new Graph(N);
            for (int i = 0; i < M; i++)
            {
                var line = Input.ReadIntArray();
                int u = line[0] - 1;
                int v = line[1] - 1;
                // 無向グラフ
                var e1 = new Edge(u, v, 0);
                G[u].Edges.Add(e1);
                G[v].InEdges.Add(e1);
                G[v].InCount++;
            }

            // トポロジカルソート
            Queue<int> q = new Queue<int>();
            for (int i = 0; i < N; i++)
            {
                if(G[i].InCount == 0) q.Enqueue(i);
            }

            List<int> topo = new List<int>();
            while (q.Count > 0)
            {
                int i = q.Dequeue();
                topo.Add(i);

                foreach (var e in G[i].Edges)
                {
                    G[e.To].InCount--;
                    if(G[e.To].InCount == 0) q.Enqueue(e.To);
                }
            }

            // argsort
            // argsはインデックスがトポロジカルソートの何番目かを表す
            int[] args = new int[N];
            for (int i = 0; i < N; i++)
            {
                args[topo[i]] = i;
            }

            // 2つある場合、一番下が親でいい
            for (int i = 0; i < N; i++)
            {
                var n = G[i];
                if (G[i].InEdges.Count == 0)
                {
                    Console.WriteLine(0);
                }
                else
                {
                    // argsが最も大きいfromをとる, +1する
                    int amax = -1;
                    int p = -1;
                    foreach (var e in n.InEdges)
                    {
                        int a = args[e.From];
                        if (a > amax)
                        {
                            amax = a;
                            p = e.From;
                        }
                    }
                    Console.WriteLine(p + 1);
                }
            }
        }

    }

    internal class Graph
    {
        public List<Node> Nodes;

        public Node this[int i]
        {
            set { Nodes[i] = value; }
            get { return Nodes[i]; }
        }

        public Graph(int N)
        {
            Nodes = new List<Node>();
            for (int i = 0; i < N; i++)
            {
                Nodes.Add(new Node(i));
            }
        }

    }

    internal class Node
    {
        public List<Edge> Edges;
        public List<Edge> InEdges;
        public int Dist;
        public int No;
        public int InCount = 0;

        public Node(int no)
        {
            this.No = no;
            Dist = int.MaxValue;
            Edges = new List<Edge>();
            InEdges = new List<Edge>();
            InCount = 0;
        }
    }

    internal class Edge
    {
        public int From;
        public int To;
        public int Cost;
        public Edge Rev;

        public Edge(int fr, int to, int cost = 0)
        {
            From = fr;
            To = to;
            Cost = cost;
        }

        public bool IsRev(Edge e)
        {
            return Rev != null && (e == Rev);
        }
    }


    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}