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 (1.42.0) (judge verdict: Time Limit Exceeded)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]
#![allow(non_snake_case)]
#![allow(unused_mut)]
#![allow(unused_variables)]
#![allow(dead_code)]

use itertools::Itertools;
use proconio::input;
use proconio::marker::{Chars, Usize1};

#[allow(unused_macros)]
#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

macro_rules! echo {
    ($($a:expr),*) => {
          $(println!("{}",$a))*
      }
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;
#[allow(dead_code)]
static M_O_D: usize = 1000000007;
#[allow(dead_code)]
static PAI: f64 = 3.1415926535897932;

trait IteratorExt: Iterator {
    fn toVec(self) -> Vec<Self::Item>;
}

impl<T: Iterator> IteratorExt for T {
    fn toVec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

trait CharExt {
    fn toNum(&self) -> usize;
    fn toAlphabetIndex(&self) -> usize;
    fn toNumIndex(&self) -> usize;
}
impl CharExt for char {
    fn toNum(&self) -> usize {
        return *self as usize;
    }
    fn toAlphabetIndex(&self) -> usize {
        return self.toNum() - 'a' as usize;
    }
    fn toNumIndex(&self) -> usize {
        return self.toNum() - '0' as usize;
    }
}

trait VectorExt {
    fn joinToString(&self, s: &str) -> String;
}
impl<T: ToString> VectorExt for Vec<T> {
    fn joinToString(&self, s: &str) -> String {
        return self
            .iter()
            .map(|x| x.to_string())
            .collect::<Vec<_>>()
            .join(s);
    }
}

trait StringExt {
    fn get_reverse(&self) -> String;
}
impl StringExt for String {
    fn get_reverse(&self) -> String {
        self.chars().rev().collect::<String>()
    }
}

trait UsizeExt {
    fn pow(&self, n: usize) -> usize;
}
impl UsizeExt for usize {
    fn pow(&self, n: usize) -> usize {
        return ((*self as u64).pow(n as u32)) as usize;
    }
}

pub struct Dikstra {
    dist: Vec<i64>,
    start: usize,
    from: Vec<usize>,
}
impl Dikstra {
    pub fn new(g: &Vec<Vec<(i64, usize)>>, start: usize) -> Self {
        let mut d = Dikstra {
            dist: vec![INF_I64; g.len()],
            start: start,
            from: vec![0; g.len()],
        };
        d.calc(g);
        return d;
    }
    fn calc(&mut self, g: &Vec<Vec<(i64, usize)>>) {
        let mut used = vec![false; g.len()];
        let mut kouho = std::collections::BinaryHeap::new();
        kouho.push((0, self.start));
        while !kouho.is_empty() {
            let (_, k) = kouho.pop().unwrap();
            used[self.start] = true;
            self.dist[self.start] = 0;
            for i in 0..g[k].len() {
                let (d, p) = g[k][i];
                if used[p] {
                    continue;
                }
                if self.dist[p] > self.dist[k] + d as i64 {
                    self.dist[p] = self.dist[k] + d as i64;
                    self.from[p] = k;
                    kouho.push((self.dist[p] * -1, p));
                }
            }
        }
    }
    pub fn dist_to(&mut self, x: usize) -> i64 {
        return self.dist[x];
    }
    pub fn from(&mut self, x: usize) -> usize {
        return self.from[x];
    }
}

fn main() {
    input! {
       N: usize,
       M:usize,
    }
    let mut map = vec![vec![]; N];
    let mut c = vec![0; N];
    for _ in 0..(N - 1 + M) {
        input! {
            a:Usize1,
            b:Usize1,
        }
        map[a].push((-1, b));
        c[b] += 1;
    }
    let mut start = c.iter().position(|&x| x == 0).unwrap();
    mydbg!(c, start);
    let mut d = Dikstra::new(&map, start);
    let mut ans = vec![0; N];
    let mut h = HashMap::new();
    for i in 0..N {
        let x = d.dist_to(i);
        let mut hp = h.entry((x * -1) as usize).or_insert(vec![]);
        hp.push(i);
    }
    for i in 0..N {
        if let Some(x) = h.get(&i) {
            for &item in x {
                ans[item] = d.from[item] + 1;
            }
        }
    }
    ans[start] = 0;

    echo!(ans.joinToString("\n"));
}