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.Collections.Generic;
using System.Linq;

public class Solution
{
    static int[] Dist;
    static int Root;
    public static int GetDistance(int p, List<int>[] upper)
    {
        if (p == Root)
        {
            return 0;
        }

        if (Dist[p] == 0)
        {
            Dist[p] = upper[p].Max(u => GetDistance(u, upper)) + 1;
        }
        return Dist[p];
    }

    public static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var n = vals[0];
        var m = vals[1];
        var edges = n - 1 + m;
        var upper = Enumerable.Range(0, n + 1).Select(_ => new List<int>()).ToArray();
        var hasParent = new bool[n + 1];
        for (int i = 0; i < edges; i++)
        {
            vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var a = vals[0];
            var b = vals[1];
            upper[b].Add(a);
            hasParent[b] = true;
        }

        Root = Enumerable.Range(1, n).First(x => !hasParent[x]);
        Dist = new int[n + 1];

        var parent = new int[n + 1];
        for (int i = 1; i <= n; i++)
        {
            if (i == Root)
            {
                parent[i] = 0;
            }
            else
            {
                parent[i] = upper[i].OrderByDescending(u => GetDistance(u, upper)).First();
            }
        }

        var answer = string.Join(Environment.NewLine, parent.Skip(1));
        Console.WriteLine(answer);
    }
}