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: Time Limit Exceeded)

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 root = -1;
            for (int i = 1; i <= N; i++) if (cntIn[i] == 0) { root = i; break; }
            var rank = new int[N + 1];
            var que = new Queue<int>();
            for (int i = 0; i < edgeOut[root].Count(); i++) que.Enqueue(edgeOut[root][i]);
            var cnt = 0;
            while (que.Any())
            {
                cnt++;
                var tmp = new Queue<int>();
                while (que.Any())
                {
                    var num = que.Dequeue();
                    rank[num] = cnt;
                    foreach (var i in edgeOut[num]) tmp.Enqueue(i);
                }
                que = tmp;
            }
            var ans = new int[N + 1];

            for (int i = 1; i <= N; i++)
            {
                var num = -1;
                var chkrank = -1;
                foreach (var j in edgeIn[i])
                {
                    if (rank[j] > chkrank)
                    {
                        num = j;
                        chkrank = rank[j];
                    }
                }
                ans[i] = num;
            }
            ans[root] = 0;

            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(); }
    }
}