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)

// たなこふ先生の input マクロ (´･_･`)
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

use std::collections::BTreeSet;
use std::collections::VecDeque;

fn topological_sort(n: usize,
                    mut incoming_edges: Vec<BTreeSet<usize>>,
                    outgoing_edges: Vec<BTreeSet<usize>>,) -> Vec<usize> {
    let mut roots = VecDeque::new();

    roots.push_back(0);

    while let Some(par) = incoming_edges[roots[0]].iter().nth(0) {
        roots[0] = *par;
    }

    let mut topological_sort = vec![n; n];
    let mut idx = 0;

    while let Some(node) = roots.pop_front() {
        for e in outgoing_edges[node].iter() {
            incoming_edges[*e].remove(&node);
            if incoming_edges[*e].is_empty() {
                roots.push_back(*e);
            }
        }
        topological_sort[node] = idx;
        idx += 1;
    }

    topological_sort
}


fn main() {
    input! {
        n: usize,
        m: usize,
        edges: [(usize1, usize1); n - 1 + m],
    }

    let (incoming_edges, outgoing_edges) = {
        let mut incoming_edges = vec![BTreeSet::<usize>::new(); n];
        let mut outgoing_edges = vec![BTreeSet::<usize>::new(); n];

        for (a, b) in edges {
            incoming_edges[b].insert(a);
            outgoing_edges[a].insert(b);
        }

        (incoming_edges, outgoing_edges)
    };

    let tsort = topological_sort(n,
                                 incoming_edges.clone(),
                                 outgoing_edges);

    for s in incoming_edges {
        if let Some(p) = s.iter().max_by(|&a, &b| tsort[*a].cmp(&tsort[*b])) {
            println!("{}", p + 1);
        } else {
            println!("0");
        }
    }
}