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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<cmath>
#include<climits>
#include<algorithm>
#include<vector>
#include<map>
#include<queue>
#include<string>
#include<set>

using namespace std;

void md(int index, vector<vector<int>> &child, vector<int> &height, vector<int> &r){
    for(int i = 0; i < child[index].size(); i++){
        r[child[index][i]]--;
        if(height[child[index][i]] < height[index] + 1){
            height[child[index][i]] = height[index] + 1;
            if(r[child[index][i]] == 0) md(child[index][i], child, height, r);
        }
    }
}



int main(void){
    int N, M;
    cin >> N >> M;
    int E = N - 1 + M;
    vector<vector<int>> child(E, vector<int>(0));
    vector<bool> isroot(E, true);
    vector<int> r(N, 0);
    for(int i = 0; i < E; i++){
        int A, B;
        cin >> A >> B;
        A--;
        B--;
        child[A].push_back(B);
        isroot[B] = false;
        r[B]++;
    }

    int root;
    for(root = 0; root < N; root++) if(isroot[root]) break;
    vector<int> height(N, -1);
    height[root] = 0;
    md(root, child, height, r);

    for(int i = 0; i < N; i++){
        for(int j = 0; j < child[i].size(); j++){
            if(height[child[i][j]] > height[i] + 1){
                child[i][j] = -1;
            }
        }
    }

    vector<int> parent(N, -1);
    for(int i = 0; i < N; i++){
        for(int j = 0; j < child[i].size(); j++){
            if(child[i][j] != -1){
                parent[child[i][j]] = i;
            }
        }
    }
     for(int i = 0; i < N; i++) cout << parent[i] + 1 << endl;
    return 0;
}