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.Text;

namespace AtTest.Nikkei2019
{
    class D
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] nm = ReadInts();
            int n = nm[0];
            int m = nm[1];
            Node[] nodes = new Node[n];
            for(int i = 0; i < n; i++)
            {
                nodes[i] = new Node();
            }
            for(int i = 0; i < n - 1 + m; i++)
            {
                int[] ab = ReadInts();
                int a = ab[0] - 1;
                int b = ab[1] - 1;
                nodes[a].outEdges.Add(b, true);
                nodes[b].inEdges.Add(a, true);
            }
            int[] parents = new int[n];
            int rootIndex = 0;
            for(int i = 0; i < n; i++)
            {
                if (nodes[i].inEdges.Count == 0)
                {
                    rootIndex = i;
                    break;
                }
            }
            Queue<int> queue = new Queue<int>();
            queue.Enqueue(rootIndex);
            parents[rootIndex] = 0;
            var visitedDict = new Dictionary<int,bool>();
            while (queue.Count > 0)
            {
                int index = queue.Dequeue();
                visitedDict.Add(index, true);
                foreach(int key in nodes[index].outEdges.Keys)
                {
                    nodes[key].inEdges.Remove(index);
                    if (nodes[key].inEdges.Count == 0)
                    {
                        parents[key] = index + 1;
                        queue.Enqueue(key);
                    }
                }
            }
            for(int i = 0; i < n; i++)
            {
                Console.WriteLine(parents[i]);
            }
        }

        class Node
        {
            public Dictionary<int, bool> inEdges;
            public Dictionary<int, bool> outEdges;
            public Node()
            {
                inEdges = new Dictionary<int, bool>();
                outEdges = new Dictionary<int, bool>();
            }
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}