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;
using System.Text;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        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); }

        static int Distance(int n, List<int>[] parents, int?[] memo)
        {
            if (!memo[n].HasValue)
            {
                memo[n] = 0;
                foreach (var parent in parents[n])
                {
                    int distance = Distance(parent, parents, memo);
                    if (distance + 1 > memo[n])
                    {
                        memo[n] = distance + 1;
                    }
                }
            }
            return memo[n].Value;
        }

        static int[] Solve(int N, int M, Tuple<int, int>[] tuples)
        {
            var parents = new List<int>[N];
            for (int i = 0; i < N; ++i)
            {
                parents[i] = new List<int>();
            }
            foreach (var tuple in tuples)
            {
                parents[tuple.Item2].Add(tuple.Item1);
            }
            var memo = new int?[N];
            var answers = Enumerable.Repeat(-1, N).ToArray();
            for (int i = 0; i < N; ++i)
            {
                int min = -1;
                foreach (var parent in parents[i])
                {
                    var distance = Distance(parent, parents, memo);
                    if (distance > min)
                    {
                        answers[i] = parent;
                        min = distance;
                    }
                }
            }
            return answers.Select(a => a + 1).ToArray();
        }

        static void Main(string[] args)
        {
            var V1 = ReadInts();
            int N = V1[0], M = V1[1];
            var tuples = new Tuple<int, int>[N + M - 1];
            for (int i = 0; i < N + M - 1; ++i)
            {
                var V2 = ReadInts();
                tuples[i] = new Tuple<int, int>(V2[0] - 1, V2[1] - 1);
            }
            foreach (var a in Solve(N, M, tuples))
            {
                Console.WriteLine(a);
            }
        }
    }
}