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 Rust (1.15.1) (judge verdict: Accepted)

use std::io;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

fn solve(i: usize, d: i32, j: usize, par: &mut Vec<usize>, depth: &mut Vec<i32>, graph: &Vec<Vec<usize>>, rgraph: &Vec<Vec<usize>>) {
    if depth[i] >= d {
        return;
    }
    if rgraph[i].len() > 1 {
        for k in rgraph[i].iter() {
            if *k != j && depth[*k] == -1 {
                return;
            }
        }
    }
    par[i] = j;
    depth[i] = d;
    for k in graph[i].iter() {
        solve(*k, d+1, i, par, depth, graph, rgraph);
    }
}

fn main() {
    let nm: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let n = nm[0];
    let m = nm[1];

    let mut graph: Vec<Vec<usize>> = vec![Vec::new(); n];
    let mut rgraph: Vec<Vec<usize>> = vec![Vec::new(); n];
    for i in 0..n+m-1 {
        let ab: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
        let a = ab[0];
        let b = ab[1];

        graph[a-1].push(b-1);
        rgraph[b-1].push(a-1);
    }

    let mut par: Vec<usize> = vec![n; n];
    let mut depth: Vec<i32> = vec![-1; n];
    for i in 0..n {
        if rgraph[i].len() == 0 {
            depth[i] = 0;
            for j in graph[i].iter() {
                solve(*j, 1, i, &mut par, &mut depth, &graph, &rgraph);
            }
            break;
        }
    }

    for i in 0..n {
        if depth[i]==0 {
            println!("{}", 0);
        } else {
            println!("{}", par[i] + 1);
        }
    }
}