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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace atcorder_Nikkei_2019
{
    class Program
    {
        struct PointData
        {
            public bool fixFlg;
            public int fixParnet;
            public int rootCnt;
            public List<int> rootList;

            public PointData(PointData pData)
            {
                // TODO: Complete member initialization
                this.fixFlg = pData.fixFlg;
                this.fixParnet = pData.fixParnet;
                this.rootCnt = pData.rootCnt;
                this.rootList = new List<int>(pData.rootList);
            }
        }
        
        struct PointMster
        {
            public List<int> parentList;
            public List<int> childList;

            public PointMster(int dummy)
            {
                // TODO: Complete member initialization
                this.parentList = new List<int>();
                this.childList = new List<int>();
            }
        }

        static PointMster[] _mstArr;
        static PointData[] _datatArr;
        static int[] _maxArr;

        static void Main(string[] args)
        {
            int[] readArr = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            int dataCnt = readArr[0];
            int addLineCnt = readArr[1];

            _mstArr = new PointMster[dataCnt + 1];
            _datatArr = new PointData[dataCnt + 1];
            _maxArr = new int[dataCnt + 1];

            //初期化
            for (int i = 1; i <= dataCnt; i++)
            {
                _mstArr[i].parentList = new List<int>();
                _mstArr[i].childList = new List<int>();
                _datatArr[i].rootList = new List<int>();
            }

            for (int i = 0; i < dataCnt + addLineCnt - 1; i++)
            {

                int[] tmp = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                _mstArr[tmp[1]].parentList.Add(tmp[0]);
                _mstArr[tmp[0]].childList.Add(tmp[1]);
            }
         
            for (int i = 1; i <= dataCnt; i++)
            {
                //未確定の場合
                if (!_datatArr[i].fixFlg)
                {
                    //スタート地点をセット
                    _datatArr[i].rootList.Add(i);
                    _datatArr[i].rootCnt++;
                    RootChek(_datatArr[i], i, i);

                    for (int j = 0; j < _datatArr[i].rootList.Count; j++)
                    {
                        //未確定のポイントのみ更新
                        if (!_datatArr[_datatArr[i].rootList[j]].fixFlg)
                        {
                            int nxtNo = _datatArr[i].rootList[j];
                            _datatArr[nxtNo].fixFlg = true;
                            if (j + 1 < _datatArr[i].rootList.Count)
                            {
                                _datatArr[nxtNo].fixParnet = _datatArr[i].rootList[j + 1];
                            }

                            if (0 == _mstArr[nxtNo].parentList.Count)
                            {
                                _datatArr[nxtNo].rootCnt = 0;
                            }
                            else
                            {
                                _datatArr[nxtNo].rootCnt = _datatArr[i].rootCnt - j;
                            }
                        }
                    }
                }
            }

            for (int i = 1; i <= dataCnt; i++)
            {
                Console.WriteLine(_datatArr[i].fixParnet);
            }
        }

        static void RootChek(PointData pData, int parNo, int startNo)
        {
            //根に到達した場合、もしくは確定ルートの場合
            if((0 == _mstArr[parNo].parentList.Count)||(_datatArr[parNo].fixFlg))
            {
                if (_datatArr[startNo].rootCnt <= pData.rootCnt)
                {
                    _datatArr[startNo] = pData;
                }
                return;
            }

            for(int i = 0; i < _mstArr[parNo].parentList.Count; i++)
            {
                int nextParNo = _mstArr[parNo].parentList[i];

                PointData tmpP = new PointData(pData);
                tmpP.rootList.Add(nextParNo);

                //確定ルートの場合
                if (_datatArr[nextParNo].fixFlg)
                {
                    tmpP.rootCnt += _datatArr[nextParNo].rootCnt;
                }
                else
                {
                    tmpP.rootCnt++;
                }

                if (tmpP.rootCnt < _maxArr[nextParNo])
                {
                    break;
                }
                else
                {
                    _maxArr[nextParNo] = tmpP.rootCnt;
                    RootChek(tmpP, nextParNo, startNo);
                }
            }

        }
    }
}