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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class MainClass
{
    static void Main()
    {
        var NM = Console.ReadLine().Split().Select(int.Parse ).ToArray();
        int N = NM[0], M = NM[1];
        var G = new List<int>[N];
        for (int i = 0; i < N; i++) G[i] = new List<int>();
        var parents = new List<int>[N];
        for (int i = 0; i < N; i++) parents[i] = new List<int>();
        var Degrees = new int[N];

        for(int i = 0; i < N+M-1; i++)
        {
            var ab = Console.ReadLine().Split().Select(_=>int.Parse(_)-1).ToArray();
            G[ab[0]].Add(ab[1]);
            Degrees[ab[1]]++;
            parents[ab[1]].Add(ab[0]);
        }

        var sorted = TopologicalSort(G, Degrees);
        var sortedpos = new int[N];
        for (int i = 0; i < N; i++)
        {
            sortedpos[sorted[i]] = i;
        }

        for (int i = 0; i < N; i++)
        {
            int parent = -1;
            int parentpos = -1;
            foreach (var vs in parents[i])
            {
                if (parentpos < sortedpos[vs])
                {
                    parent = vs;
                    parentpos = sortedpos[vs];
                }

            }

            Console.WriteLine(parent+1);
        }
    }
    static List<int> TopologicalSort(List<int>[] G,int[] Degrees)
    {
        var que = new Queue<int>();
        for (int i = 0; i < Degrees.Length; i++)
        {
            if (Degrees[i] == 0)
                que.Enqueue(i);
        }

        List<int> sorted = new List<int>();
        while (que.Count > 0)
        {
            var t = que.Dequeue();
            sorted.Add(t);

            foreach (var i in G[t])
            {
                Degrees[i]--;
                if (Degrees[i] == 0)
                {
                    que.Enqueue(i);
                }
            }
        }

        return sorted;
    }
}