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: Accepted)

#include "bits/stdc++.h"
#pragma GCC optimize("Ofast")

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) x.begin(), x.end()
#define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
#define reps(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__)

constexpr size_t    operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t  operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

template <class T, class Compare = less<>>
using MaxHeap = priority_queue<T, vector<T>, Compare>;
template <class T, class Compare = greater<>>
using MinHeap = priority_queue<T, vector<T>, Compare>;

inline void input() {}
template <class Head, class... Tail>
inline void input(Head&& head, Tail&&... tail) {
    cin >> head;
    input(forward<Tail>(tail)...);
}

template <class T>
inline istream& operator>>(istream &is, vector<T> &vec) {
    for (auto &e: vec) {
        is >> e;
    }
    return is;
}

inline void output() { cout << "\n"; }
template <class Head, class... Tail>
inline void output(Head&& head, Tail&&... tail) {
    cout << head;
    if (sizeof...(tail)) {
        cout << " ";
    }
    output(forward<Tail>(tail)...);
}

template <class T>
inline ostream& operator<<(ostream &os, const vector<T> &vec) {
    static constexpr const char *delim[] = {" ", ""};
    for (const auto &e: vec) {
        os << e << delim[&e == &vec.back()];
    }
    return os;
}

template <class T>
inline vector<T> makeVector(const T &initValue, size_t sz) {
    return vector<T>(sz, initValue);
}

template <class T, class... Args>
inline auto makeVector(const T &initValue, size_t sz, Args... args) {
    return vector<decltype(makeVector<T>(initValue, args...))>(sz, makeVector<T>(initValue, args...));
}

template <class Func>
class FixPoint : Func {
public:
    explicit constexpr FixPoint(Func&& f) noexcept : Func(forward<Func>(f)) {}

    template <class... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return Func::operator()(*this, std::forward<Args>(args)...);
    }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept {
    return FixPoint<Func>{forward<Func>(f)};
}

template <class Container>
struct reverse_t {
    Container &c;
    reverse_t(Container &c) : c(c) {}
    auto begin() { return c.rbegin(); }
    auto end() { return c.rend(); }
};

template <class Container>
auto reversed(Container &c) {
    return reverse_t<Container>(c);
}

template <class T>
inline bool chmax(T &a, const T &b) noexcept {
    return b > a && (a = b, true);
}

template <class T>
inline bool chmin(T &a, const T &b) noexcept {
    return b < a && (a = b, true);
}

template <class T>
inline T diff(const T &a, const T &b) noexcept {
    return a < b ? b - a : a - b;
}
// End Header }}}

// Edge {{{
template <class Weight>
struct Edge {
    size_t from, to;
    Weight weight;

    Edge() {}
    Edge(size_t from, size_t to, Weight weight = 1) :
        from(from), to(to), weight(weight)
    {}

    bool operator<(const Edge &rhs) const {
        return weight < rhs.weight;
    }

    bool operator>(const Edge &rhs) const {
        return weight > rhs.weight;
    }

    operator size_t() const {
        return to;
    }
};
// }}}

// Graph {{{
template <class Weight>
class Graph : public vector<vector<Edge<Weight>>> {
    using graph = vector<vector<Edge<Weight>>>;

public:
    Graph() {}
    Graph(const size_t V) : graph(V) {}

    void connect(size_t from, size_t to, Weight weight = 1) {
        (*this)[from].emplace_back(from, to, weight);
    }

    friend ostream& operator<<(ostream &strm, const Graph &G) {
        for (size_t v = 0; v < G.size(); ++v) {
            strm << '[' << setw(2) << v << ']';
            for (const auto &e: G[v]) {
                strm << ' ' << setw(2) << e.to;
            }
            strm << '\n';
        }
        return strm;
    }
};
// }}}

// topologicalSort {{{
template <class T>
vector<size_t> topologicalSort(const Graph<T> &G) {
    const size_t N = G.size();
    vector<size_t> ord, indeg(N);
    queue<size_t> que;
    ord.reserve(N);
    for (size_t v = 0; v < N; ++v) {
        for (const auto e: G[v]) {
            indeg[e.to]++;
        }
    }
    for (size_t v = 0; v < N; ++v) {
        if (indeg[v] == 0) {
            que.push(v);
        }
    }
    while (!que.empty()) {
        const size_t cur = que.front();
        que.pop();
        ord.push_back(cur);
        for (const auto e: G[cur]) {
            if (--indeg[e.to] == 0) {
                que.push(e.to);
            }
        }
    }
    return ord;
}
// }}}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.setf(ios_base::fixed);
    cout.precision(10);
    var(size_t, N, M);
    Graph<size_t> G(N);
    rep(i, 0, N - 1 + M) {
        var(size_t, a, b);
        a--, b--;
        G.connect(a, b);
    }
    const auto vs = topologicalSort(G);
    vector<size_t> res(N);
    for (const auto v: vs) {
        for (const auto e: G[v]) {
            res[e.to] = v + 1;
        }
    }
    for (const auto e: res) output(e);
    return 0;
}