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++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <map>
#include <queue>
#include <deque>
#include <string>
#include <stack>
#include <vector>
#include <set>
#include <tuple>
#include <utility>
#include <functional>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
typedef tuple<int,int,int> T;
const int INF = 1000000000;
const int MOD = 1000000007;
struct edge{int from,to,cost;};
int main(){
	int n,m;
	cin >> n >> m;
	vector<edge> es;
	vector<int> d(n);
	for(int i = 0;i < n;i++)d[i] = 0;

	vector<int> in_deg(n,0);
	for(int i = 0;i < n - 1 + m;i++){
		int a,b;
		cin >> a >> b;
		a--,b--;
		es.push_back(edge{a,b,1});
		in_deg[b]++;
	}

	int s;
	for(int i = 0;i < n;i++){
		if(in_deg[i] == 0)s = i;
	}

	d[s] = 0;
	vector<int> par(n,0);
	while(true){
		bool update = false;
		for(int i = 0;i < es.size();i++){
			edge e = es[i];
			if(d[e.to] < d[e.from] + e.cost){
				d[e.to] = d[e.from] + e.cost;
				par[e.to] = e.from + 1;
				update = true;
			}
		}
		if(!update)break;
	}
	

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