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.Web;
using System.IO;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Linq;
using System.Numerics;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using static System.Math;
 

class P
{
    static void Main()
    {
        int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        List<int>[] edge = Enumerable.Repeat(0, nm[0]).Select(_ => new List<int>()).ToArray();
        List<int>[] revedge = Enumerable.Repeat(0, nm[0]).Select(_ => new List<int>()).ToArray();

        int all = nm[0] - 1 + nm[1];
        for (int i = 0; i < all; i++)
        {
            int[] ab =Console.ReadLine().Split().Select(int.Parse).ToArray();
            revedge[ab[0] - 1].Add(ab[1] - 1);
            edge[ab[1] - 1].Add(ab[0] - 1);
        }
        //あー、復元ね。
        //BFSした時に一番遅く到達した奴が勝ち
        int root = 0;
        while (edge[root].Count != 0)
        {
            root = edge[root][0];
        }
        Debug.WriteLine($"root : {root}");
        int[] allparents = new int[nm[0]];
        Queue<int> queue = new Queue<int>();
        queue.Enqueue(root);
        while (queue.Count != 0)
        {
            var elem = queue.Dequeue();
            foreach (var child in revedge[elem])
            {
                allparents[child] = elem + 1;
                queue.Enqueue(child);
            }
        }
        Console.WriteLine(string.Join("\n", allparents));
    }
}