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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.HashSet;

public class Main
{

  public static void main(String[] args) throws IOException
  {
    BufferedReader r = new BufferedReader(new InputStreamReader(System.in), 1);
    String s = r.readLine();
    String[] sl = s.split(" ");
    int n = Integer.parseInt(sl[0]);
    int m = Integer.parseInt(sl[1]);
    ArrayList<ArrayList<Integer>> g = new ArrayList<>();
    int prof[] = new int[n + 1];
    int schd[] = new int[n + 1];
    g.add(new ArrayList<Integer>());
    HashSet<Integer> set = new HashSet<>();
    for(int i = 1; i <= n; i++)
    {
      g.add(new ArrayList<Integer>());
      set.add(i);
    }

    for(int i = 0; i < n - 1 + m; i++)
    {
      s = r.readLine();
      sl = s.split(" ");
      int a = Integer.parseInt(sl[0]);
      int b = Integer.parseInt(sl[1]);
      g.get(a).add(b);
      set.remove(b);
    }
    Object[] rs = set.toArray();
    int root = (int)rs[0];

    //System.out.println(root);
    ArrayDeque<Integer> q = new ArrayDeque<>();

    q.add(root);
    while(!q.isEmpty())
    {
      int proc = q.pop();
      schd[proc] = 1;
      for(Integer e : g.get(proc))
      {
        prof[e] = proc;
        if(schd[e] == 0)
          q.add(e);
      }
    }

    for(int i = 1; i <= n; i++)
    {
      System.out.println(prof[i]);
    }
  }


}