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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"bytes"
	"fmt"
	"os"
	"strconv"
)

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	var N, M int
	scanner.Scan()
	fmt.Sscanf(scanner.Text(), "%d %d", &N, &M)

	edges := make(map[int][]int)
	redges := make(map[int][]int)
	inCnt := make(map[int]int)
	for i := 0; i < N-1+M; i++ {
		var from, to int
		scanner.Scan()
		fmt.Sscanf(scanner.Text(), "%d %d", &from, &to)
		edges[from] = append(edges[from], to)
		redges[to] = append(redges[to], from)
		inCnt[to]++
	}

	root := -1
	for i := 1; i <= N; i++ {
		if inCnt[i] == 0 {
			root = i
			break
		}
	}

	tpsorted := make([]int, 0)
	workList := make([]int, 0)
	left, right := 0, 0
	workList = append(workList, root)
	right++
	for left < right {
		// remove node
		node := workList[left]
		left++
		// add node
		tpsorted = append(tpsorted, node)
		for _, to := range edges[node] {
			inCnt[to]--
			if inCnt[to] == 0 {
				workList = append(workList, to)
				right++
			}
		}
	}

	node2order := make(map[int]int)
	for i, node := range tpsorted {
		node2order[node] = i
	}

	var buffer bytes.Buffer
	for i := 1; i <= N; i++ {
		if i == root {
			buffer.WriteString("0\n")
		} else if len(redges[i]) == 1 {
			buffer.WriteString(strconv.Itoa(redges[i][0]))
			buffer.WriteString("\n")
		} else {
			tmpOrder := -1
			tmpNode := -1
			for _, from := range redges[i] {
				order := node2order[from]
				if order > tmpOrder {
					tmpOrder = order
					tmpNode = from
				}
			}
			buffer.WriteString(strconv.Itoa(tmpNode))
			buffer.WriteString("\n")
		}
	}
	fmt.Println(buffer.String())
}