OI XXVIII - zdj

// https://szkopul.edu.pl/problemset/problem/GfCNwxdYubiS1Nlnb_h7VkJW/site/?key=statement

#include <bits/stdc++.h>

// #define GARY_DBG
#define GARY_LIB

constexpr int sizik = 500 * 1001;

#define ar std::array

typedef std::vector<std::vector<int>> _kra;

int deg[sizik];
std::vector<int> kra[sizik];
std::vector<int> kra1[sizik];
int in_cnt[sizik];

std::pair<int, int> create_pair(int a, int b) {
    if (a > b) std::swap(a, b);
    return std::make_pair(a, b);
}

void not_good() {
    std::cout << "NIE\n";
}

void solve() {
    int n, m;
    std::cin >> n >> m;

    std::vector<ar<int, 2>> kraw(m);

    for (auto& [a, b] : kraw) {
        std::cin >> a >> b;

        kra[a].push_back(b);
        kra[b].push_back(a);

        deg[a]++;
        deg[b]++;
    }

    if (m == 0) {
        std::cout << "TAK\n";
        for (int i = 1; i <= n; i++) {
            std::cout << i << ' ';
        }
        std::cout << '\n';
        return;
    }

    if (deg[1] == 0 || deg[2] == 0) {
        not_good();
        return;
    }

    std::map<std::pair<int, int>, bool> mp;

    std::queue<int> q;
    q.push(1);
    int g = 0;
    while (!q.empty()) {
        int v = q.front();
        q.pop();

        for (const auto& u : kra[v]) {
            auto p = create_pair(v, u);
            if (!mp[p]) {
                g++;
                mp[p] = 1;
                kra1[v].push_back(u);
                in_cnt[u]++;
                if (u != 2 && 2 * in_cnt[u] > deg[u]) {
                    not_good();
                    return;
                }
                if (u != 2 && 2 * in_cnt[u] == deg[u]) {
                    q.push(u);
                }
            }
        }
    }

    if (g != m) {
        not_good();
        return;
    }

    while (!q.empty()) {
        q.pop();
    }

    std::vector<int> topo_kol;
    topo_kol.reserve(n);

    std::vector<int> izolaki;
    izolaki.reserve(n);
    for (int i = 3; i <= n; i++) {
        if (in_cnt[i] == 0) {
            izolaki.push_back(i);
        }
    }

    q.push(1);

    while (!q.empty()) {
        int v = q.front();
        q.pop();

        topo_kol.push_back(v);

        for (const auto& u : kra1[v]) {
            if (--in_cnt[u] == 0) {
                q.push(u);
            }
        }
    }

    if ((izolaki.size() + topo_kol.size()) != n) {
        not_good();
        return;
    }

    int last = 1;
    std::vector<int> ans(n + 1);
    for (const auto& x : topo_kol) {
        ans[x] = last++;
    }
    for (const auto& x : izolaki) {
        ans[x] = last++;
    }

    std::cout << "TAK\n";
    for (int i = 1; i <= n; i++) {
        std::cout << ans[i] << ' ';
    }
    std::cout << '\n';
}

int32_t main() {
#ifndef GARY_DBG
    std::ios_base::sync_with_stdio(0);
    std::cin.tie(0);
    std::cout.tie(0);
#endif

    int t = 1;
    // std::cin >> t;

    for (; t > 0; t--) {
        solve();
    }

    return 0;
}