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.Linq;
using System.Collections.Generic;
class c
{
    static void Main()
    {
        var nm = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int n = nm[0], m = nm[1];
        var list = new List<Tuple<int, int>>();
        for (int i = 0; i < n + m - 1; i++)
        {
            var line = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            list.Add(new Tuple<int, int>(line[0], line[1]));
        }

        for (int i = 1; i <= n; i++)
        {
            var tree = new int[n + 1];
            tree[0] = -2;
            tree[i] = -1;
            int edge = 0;
            var Q = new List<int>();
            Q.Add(i);
            while (Q.Any())
            {
                for (int j = 0; j < n + m - 1; j++)
                {
                    if (list[j].Item1 == Q[0])
                    {
                        tree[list[j].Item2] = Q[0];
                        edge++;
                        Q.Add(list[j].Item2);
                    }
                }
                Q.Remove(Q[0]);
            }
            if (!tree.Contains(0))
            {
                foreach (var x in tree)
                {
                    if (x == -2) continue;
                    Console.WriteLine(x == -1 ? 0 : x);
                }
                break;
            }
        }
    }
}