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.Generic;
using System.IO;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var M = sc.ReadInt();
        var AB = sc.ReadTupArray(N + M - 1, -1);
        var g = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            g[i] = new List<int>();
        }
        var tp = new Topological(N);
        for (int i = 0; i < N + M - 1; i++)
        {
            var a = AB[i].Item1;
            var b = AB[i].Item2;
            g[a].Add(b);
            tp.Add(a, b, -1);
        }
        var root = Enumerable.Range(0, N).Except(AB.Select(ab => ab.Item2)).First();
        var dist = tp.GetMinCost(root);
        var edges = new List<Tuple<int, int>>();
        var q = new Queue<Tuple<int, int>>();
        q.Enqueue(Tuple.Create(root, 0));
        while (q.Count > 0)
        {
            var t = q.Dequeue();
            var now = t.Item1;
            var d = t.Item2;
            if (d == -dist[now])
            {
                foreach (var next in g[now])
                {
                    if (-dist[next] == d + 1)
                    {
                        edges.Add(Tuple.Create(now, next));
                        q.Enqueue(Tuple.Create(next, d + 1));
                    }
                }
            }
        }
        edges.Add(Tuple.Create(-1, root));
        foreach (var e in edges.OrderBy(e => e.Item2))
        {
            Console.WriteLine(e.Item1 + 1);
        }
    }
    static Scanner sc = new Scanner();
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<long, long> ReadTupLong(int add = 0)
    {
        return Tuple.Create(this.ReadLong() + add, this.ReadLong() + add);
    }
    public Tuple<int, int, int> ReadTup3(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public Tuple<int, int, int, int> ReadTup4(int add = 0)
    {
        return Tuple.Create(this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add, this.ReadInt() + add);
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n, int add = 0)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong(add);
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n, int add = 0)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup(add);
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3(add);
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n, int add = 0)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4(add);
        }
        return array;
    }
}


class Topological
{
    public List<Edge>[] Dag { get; set; }
    public int[] CountIn { get; set; }
    public int N { get; set; }
    public Topological(int n)
    {
        this.N = n;
        this.Dag = new List<Edge>[n];
        for (int i = 0; i < n; i++)
        {
            this.Dag[i] = new List<Edge>();
        }
        this.CountIn = new int[n];
    }
    public void Add(int a, int b, long cost)
    {
        this.Dag[a].Add(new Edge(b, cost));
        this.CountIn[b]++;
    }
    public int[] Sort()
    {
        int[] countIn = new int[N];
        for (int i = 0; i < N; i++) countIn[i] = this.CountIn[i];
        var q = new Queue<int>();
        for (int i = 0; i < N; i++)
        {
            if (countIn[i] == 0) q.Enqueue(i);
        }
        var list = new List<int>();
        while (q.Count > 0)
        {
            var now = q.Dequeue();
            list.Add(now);
            foreach (var e in this.Dag[now])
            {
                countIn[e.To]--;
                if (countIn[e.To] == 0) q.Enqueue(e.To);
            }
        }
        return list.ToArray();
    }
    public long[] GetMinCost(int start)
    {
        var sorted = this.Sort();
        var dist = new long[this.N];
        for (int i = 0; i < N; i++)
        {
            dist[i] = int.MaxValue;
        }
        dist[start] = 0;
        for (int i = 0; i < N - 1; i++)
        {
            var now = sorted[i];
            foreach (var e in Dag[now])
            {
                dist[e.To] = Math.Min(dist[e.To], dist[now] + e.Cost);
            }
        }
        return dist;
    }
    public struct Edge
    {
        public int To { get; set; }
        public long Cost { get; set; }
        public Edge(int to, long cost)
        {
            this.To = to;
            this.Cost = cost;
        }
    }
}