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.Linq;

namespace 日経PC2019_D___Restore_the_Tree
{
    class Program
    {
        static void Main(string[] args)
        {
            var NM = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var N = NM[0]; var M = NM[1];
            var to = new List<int>[N + 1];
            for (int i = 0; i < N + 1;i++)to[i] = new List<int>();
            var indegree = new int[N + 1];
            indegree[0] = -1;
            for (int i = 0; i < N + M - 1; i++)
            {
                var ab = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                to[ab[0]].Add(ab[1]);
                indegree[ab[1]]++;
            }

            var queue = new Queue<int>();
            int root = 1;
            for (; root < N + 1; root++) if (indegree[root] == 0) break;
            var parents = new int[N + 1];
            parents[root] = 0;
            queue.Enqueue(root);
            while (queue.Count > 0)
            {
                var parent = queue.Dequeue();
                foreach (int e in to[parent])
                {
                    indegree[e]--;
                    if (indegree[e] == 0)
                    {
                        parents[e] = parent;
                        queue.Enqueue(e);
                    }
                }
            }

            for (int i = 1; i < N + 1; i++) Console.WriteLine(parents[i]);
        }
    }
}