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 test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadArrayInt();
            var N = input[0];
            var M = input[1];
            var edgeOut = new List<int>[N + 1].Select(e => new List<int>()).ToArray();
            var edgeIn = new List<int>[N + 1].Select(e => new List<int>()).ToArray();
            var cntIn = new int[N + 1];
            for (int i = 0; i < N - 1 + M; i++)
            {
                input = ReadArrayInt();
                var A = input[0];
                var B = input[1];
                edgeOut[A].Add(B);
                edgeIn[B].Add(A);
                cntIn[B]++;
            }
            var zero = new Queue<int>();
            for (int i = 1; i <= N; i++) if (cntIn[i] == 0) { zero.Enqueue(i); break; }
            var seq = new List<int>();
            var cnt = 0;
            var idx = new int[N + 1];
            while (zero.Any())
            {
                var num = zero.Dequeue();
                seq.Add(num);
                idx[num] = cnt;
                cnt++;
                foreach(var i in edgeOut[num])
                {
                    cntIn[i]--;
                    if (cntIn[i] == 0) zero.Enqueue(i);
                }
            }
            var ans = new int[N + 1];
            ans[seq[0]] = 0;
            for (int i = 1; i < seq.Count(); i++)
            {
                var max = -1;
                var ret = -1;
                foreach (var j in edgeIn[seq[i]])
                {
                    if (idx[j] > max)
                    {
                        max = idx[j];
                        ret = j;
                    }
                }
                ans[seq[i]] = ret;
            }

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

            Console.WriteLine();
            Console.ReadLine();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}