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 Scala (2.11.7) (judge verdict: Runtime Error)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.Queue
import scala.collection.mutable.PriorityQueue

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)


  val V, M = in.next().toInt
  val E = V-1 + M

  val graph = Array.fill[List[Int]](V+1)(Nil) // 隣接リスト

  // input
  for (_ <- 1 to E) {
    val a, b = in.next().toInt
    graph(b) = a :: graph(b)
  }

  //
  val dp = Array.fill[Int](V+1)(-1)
  val ans = new Array[Int](V+1)

  def func(v: Int): Int = {
    if(dp(v) != -1)
      dp(v)
    else {
      if(graph(v).isEmpty) {
        dp(v) = 0
      }
      else {
        for (e <- graph(v)) {
          val now = func(e) + 1
          if(now > dp(v)) {
            dp(v) = now
            ans(v) = e
          }
        }
      }
      dp(v)
    }
  }

  for (i <- 1 to V)
    func(i)

  ans.tail.foreach { pw.println }
  pw.flush()
}


class InputReader(stream: InputStream) {
  private val reader = new BufferedReader(new InputStreamReader(stream))
  private var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}