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: Accepted)

#include "bits/stdc++.h"

using namespace std;

using ll = long long;
using ld = long double;
using P = pair<ll, ll>;
constexpr ld EPS = 1e-12;
constexpr int INF = numeric_limits<int>::max() / 2;
constexpr int MOD = 1e9 + 7;

template <typename T>
void printv(const vector<T> &v)
{
    int sz = v.size();
    for (int i = 0; i < sz; i++)
    {
        cout << v[i] << " \n"[i == sz - 1];
    }
}

using Graph = vector<vector<int>>;

void dfs(int v, const Graph &G, vector<int> &res, vector<int> &used)
{
    used[v] = 1;
    for (auto to : G[v])
        if (used[to] == 0)
        {
            dfs(to, G, res, used);
        }
    res.push_back(v);
}

vector<int> topo_sort(const Graph &G)
{
    int V = G.size();
    vector<int> ide(V);
    for (int i = 0; i < V; i++)
    {
        for (auto to : G[i])
        {
            ide[to]++;
        }
    }
    vector<int> res;
    vector<int> used(V);
    for (int i = V - 1; i >= 0; i--)
    {
        if (ide[i] == 0)
        {
            dfs(i, G, res, used);
        }
    }
    if (res.size() == 0)
        res = {-1};
    reverse(res.begin(), res.end());
    return res;
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n, m;
    cin >> n >> m;
    Graph g(n), rev(n);
    for (int i = 0; i < n - 1 + m; i++)
    {
        int a, b;
        cin >> a >> b;
        a--;
        b--;
        g[a].push_back(b);
        rev[b].push_back(a);
    }
    vector<int> ts = topo_sort(g);
    vector<int> res(n, -1), pri(n);
    for (int i = 0; i < n; i++)
        pri[ts[i]] = i;
    res[ts[0]] = 0;
    for (int i = n - 1; i > 0; i--)
    {
        int v = ts[i];
        int ma = -1, idx = -1;
        for (auto u : rev[v])
        {
            if (pri[u] > ma)
            {
                ma = pri[u];
                idx = u;
            }
        }
        res[v] = idx + 1;
    }
    for (int i = 0; i < n; i++)
    {
        cout << res[i] << endl;
    }
}