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: Accepted)

use proconio::input;
use proconio::marker::Usize1;
use std::collections::VecDeque;

struct Node {
    to: Vec<usize>,
    from: Vec<usize>,
}

impl Node {
    fn new() -> Self
    {
        Node {
            to: Vec::new(),
            from: Vec::new(),
        }
    }
}

fn main() {
    input! {
    n:usize,
    m:usize,
    edge:[(Usize1,Usize1);n+m-1],
    }

    let mut node = (0..n).map(|_| Node::new()).collect::<Vec<Node>>();
    for (a, b) in edge {
        node[a].to.push(b);
        node[b].from.push(a);
    }

    let mut cnt = vec![0; n];
    let mut ans = vec![0; n];

    let mut q = VecDeque::new();
    let root = node.iter().position(|n| n.from.len() == 0).unwrap();
    q.push_back(root);

    while let Some(idx) = q.pop_front() {
        for i in 0..node[idx].to.len() {
            let nxt = node[idx].to[i];
            cnt[nxt] += 1;
            if cnt[nxt] == node[nxt].from.len() {
                ans[nxt] = idx + 1;
                q.push_back(nxt);
            }
        }
    }

    for i in ans {
        println!("{}", i);
    }
}