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: Runtime Error)

import java.util.Scanner;
import java.util.Stack;

public class Main {

	private static int max = 0;
	private static int count = 0;
	static Stack<Integer> list = new Stack<Integer>();

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int m = scan.nextInt();
		int[][] arr01 = new int[n + 1][n + 1];
		for (int i = 1; i <= n + m - 1; i++) {
			arr01[scan.nextInt()][scan.nextInt()] = 1;
		}
		int[][] ans = new int[n + 1][n + 1];
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= n; j++) {
				if (arr01[j][i] != 0) {
					ans[j][i] = max(arr01, i, j);
					max = 0;
					count = 0;
				}
			}
		}
		for (int i = 1; i <= n; i++) {
			System.out.println(maxPath(ans, i));
		}
		scan.close();
	}

	private static int max(int[][] arr01, int col, int row) {

		count++;
		list.add(row);
		for (int i = 1; i < arr01.length; i++) {
			if (arr01[i][row] != 0) {
				max(arr01, row, i);
			}
		}

		if (count > max) {
			max = count;
		}
		count--;
		list.pop();

		return max;

	}

	private static int maxPath(int ans[][], int col) {
		int max = 0;
		int ret = 0;
		for (int i = 1; i < ans.length; i++) {
			if (ans[i][col] > max) {
				max = ans[i][col];
				ret = i;
			}
		}
		return ret;
	}
}