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.util.*;

public class Main {

    static class Node {
        int parent;
        HashSet<Integer> neighbors;
        HashSet<Integer> children;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        ArrayList<HashSet<Integer>> edge = new ArrayList<HashSet<Integer>>();
        for (int i=0;i<N;i++) {
            HashSet<Integer> add = new HashSet<Integer>();
            edge.add(add);
        }
        boolean[] root_find = new boolean[N];
        for (int i=0;i<N-1+M;i++) {
            int A = sc.nextInt()-1;
            int B = sc.nextInt()-1;
            root_find[B] = true;
            edge.get(A).add(B);
        }
        int root = -1;
        for (int i=0;i<N;i++) if (!root_find[i]) root=i;

        // ArrayList<Node> list = new ArrayList<Node>();
        int[] parent = new int[N];
        Arrays.fill(parent, -2);
        parent[root] = -1;
        ArrayDeque<Integer> q = new ArrayDeque<Integer>();
        q.add(root);
        while (!q.isEmpty()) {
            int rem = q.poll();
            // if (parent[root]>=0) {
            // }
            for (Integer i : edge.get(rem)) {
                if (parent[i]<0) q.add(i);
                parent[i] = rem;
            }
        }
        for (int i=0;i<N;i++) {
            System.out.println(parent[i]+1);
        }
    }
}