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)

// Try NIKKEI Programming Contest 2019
// author: Leonardone @ NEETSDKASU

fn main() {
    let mut stdin = String::new();
    std::io::Read::read_to_string(
        &mut std::io::stdin(),
        &mut stdin).unwrap();
    let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    macro_rules! get {
        ($t:ty) => (get().parse::<$t>().unwrap());
        () => (get!(usize));
    }
    
    let n = get!();
    let m = get!();
    let mut tree = vec![vec![]; n];
    let mut undi = vec![vec![]; n];
    let mut cnt = vec![0_i32; n];
    let mut pair = vec![std::usize::MAX; n];
    for _ in 0..n+m-1 {
        let a = get!() - 1;
        let b = get!() - 1;
        cnt[a] += 1;
        tree[a].push(b);
        undi[b].push(a);
    }
    
    let mut ps = vec![];
    
    for i in 0..n {
        if cnt[i] == 0 {
            ps.push(i);
        }
    }
    
    while !ps.is_empty() {
        for &p in ps.iter() {
            for &t in tree[p].iter() {
                if cnt[t] == 0 {
                    cnt[t] = -1;
                    pair[t] = p;
               }
            }
        }
        let mut es = vec![];
        for &p in ps.iter() {
            for &u in undi[p].iter() {
                cnt[u] -= 1;
                if cnt[u] == 0 {
                    es.push(u);
                }
            }
        }
        ps = es;
    }
    for &p in pair.iter() {
        if p == std::usize::MAX {
            println!("0");
        } else {
            println!("{}", p + 1);
        }
    }
}