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 <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <deque>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <ctime>
#include <iterator>
#include <bitset>
#include <numeric>
#include <list>
#include <iomanip>
using namespace std;
#define ll int64_t
const long MOD = 1e9 + 7;
const long LINF = 1e13;
const long LLINF = 1e18;
const long ALPHABET = 26;

template <class T>
void Swap(T& r, T& l) {
  T tmp = r;
  r = l;
  l = tmp;
}



int main() {

  long n, m;
  cin >> n >> m;

  vector<pair<long,long>> arc(n - 1 + m);

  vector<vector<long>> arc_from_node_i(n);
  vector<vector<long>> arc_to_node_i(n);

  vector<long> a(n - 1 + m);
  vector<long> b(n - 1 + m);
  for (int i = 0; i < n - 1 + m; i++) {
    cin >> a[i] >>  b[i];
    a[i]--;
    b[i]--;

    arc_from_node_i[a[i]].push_back(b[i]);
    arc_to_node_i[b[i]].push_back(a[i]);
  }

  for (int i = 0; i < n; i++) {
    cerr << i << "  :";
    for(auto v :arc_from_node_i[i] ){
      cerr << v <<",";
    }cerr <<endl;
  }


  long rootnode = 0;
  for (int i = 0; i < n; i++) {
    if (arc_to_node_i[i].size() ==0)rootnode = i;
  }

  cerr <<"root : "<<rootnode <<endl;

  vector<long> ans(n, 0);


  ans[rootnode] = -1;

  vector<long> li;
  for(auto v:arc_from_node_i[rootnode]){
    li.push_back(v);
    ans[v] = rootnode;
  }

  while(li.size() > 0){
    vector<long> li2;
    for(auto v:li){
      for(auto i:arc_from_node_i[v]){
        ans[i] = v;
      }
    }

    li.clear();
    for(auto v:li2){
      li.push_back(v);
    }
    
  }


  for (int i = 0; i < n; i++) {
    cout << ans[i]+1 << endl;
  }


}