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::str::FromStr;
use std::collections::VecDeque;

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut g: Vec<Vec<usize>> = vec![Vec::new(); n];
    let mut rev_g: Vec<Vec<usize>> = vec![Vec::new(); n];
    for _ in 0..n+m-1 {
        let a = read::<usize>()-1;
        let b = read::<usize>()-1;
        g[a].push(b);
        rev_g[b].push(a);
    }
    let mut que: VecDeque<usize> = VecDeque::new();
    let mut root = 0;
    let mut cnt: Vec<usize> = vec![0; n];
    for i in 0..n {
        cnt[i] += rev_g[i].len();
        if rev_g[i].is_empty() {
            root = i;
        }
    }
    let mut ans: Vec<usize> = vec![0; n];
    que.push_back(root);
    while let Some(q) = que.pop_front() {
        for i in &g[q] {
            if cnt[*i] > 1 {
                cnt[*i] -= 1;
            } else {
                ans[*i] = q+1;
                que.push_back(*i);
            }
        }
    }
    for i in 0..n {
        println!("{}", ans[i]);
    }
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}