OI XXXI - prz (Alt)

// https://szkopul.edu.pl/problemset/problem/eQ4z7Bnhqsl67nKb_NlISLNZ/site/?key=statement

#include <bits/stdc++.h>

const int MAXN = 200005;

struct Edge {
    int to;
    int id;
};

int n, m;
std::vector<Edge> adj[MAXN];
int vis[MAXN];

int parent_node[MAXN];
int parent_edge[MAXN];
bool found_cycle = false;
int cycle_start = -1, cycle_end = -1, cycle_closing_edge = -1;

int deg[MAXN];
std::vector<int> solution_edges;

void dfs_cycle(int u, int p) {
    vis[u] = 1;
    for (auto& e : adj[u]) {
        int v = e.to;
        if (v == p) continue;

        if (vis[v] == 1) {
            found_cycle = true;
            cycle_start = v;
            cycle_end = u;
            cycle_closing_edge = e.id;
            return;
        }

        if (vis[v] == 0) {
            parent_node[v] = u;
            parent_edge[v] = e.id;
            dfs_cycle(v, u);
            if (found_cycle) return;
        }
    }
    vis[u] = 2;
}

void dfs_parity(int u, int p, int edge_from_p) {
    vis[u] = 1;
    for (auto& e : adj[u]) {
        int v = e.to;
        if (v != p) {
            dfs_parity(v, u, e.id);
        }
    }

    if (deg[u] % 2 == 0) {
        if (p != -1) {
            deg[u]++;
            deg[p]++;
            solution_edges.push_back(edge_from_p);
        }
    }
}

int main() {
    std::ios_base::sync_with_stdio(0);
    std::cin.tie(0);
    std::cout.tie(0);

    std::cin >> n >> m;

    for (int i = 1; i <= m; ++i) {
        int r, c;
        std::cin >> r >> c;
        int u = r;
        int v = n + c;
        adj[u].push_back({v, i});
        adj[v].push_back({u, i});
    }

    std::fill(vis, vis + 2 * n + 1, 0);
    for (int i = 1; i <= 2 * n; ++i) {
        if (!vis[i]) {
            dfs_cycle(i, -1);
            if (found_cycle) break;
        }
    }

    if (found_cycle) {
        std::cout << "TAK\n";
        std::vector<int> cycle_path;
        cycle_path.push_back(cycle_closing_edge);

        int curr = cycle_end;
        while (curr != cycle_start) {
            cycle_path.push_back(parent_edge[curr]);
            curr = parent_node[curr];
        }

        std::cout << cycle_path.size() << "\n";
        for (int i = 0; i < cycle_path.size(); ++i) {
            std::cout << cycle_path[i] << (i == cycle_path.size() - 1 ? "" : " ");
        }
        std::cout << "\n";
        return 0;
    }

    std::fill(vis, vis + 2 * n + 1, 0);
    std::fill(deg, deg + 2 * n + 1, 0);
    solution_edges.clear();

    for (int i = 1; i <= 2 * n; ++i) {
        if (!vis[i]) {
            dfs_parity(i, -1, -1);
        }
    }

    bool ok = true;
    if (solution_edges.empty()) ok = false;

    for (int i = 1; i <= 2 * n; ++i) {
        if (deg[i] % 2 == 0) {
            ok = false;
            break;
        }
    }

    if (ok) {
        std::cout << "TAK\n";
        std::cout << solution_edges.size() << "\n";
        for (int i = 0; i < solution_edges.size(); ++i) {
            std::cout << solution_edges[i] << (i == solution_edges.size() - 1 ? "" : " ");
        }
        std::cout << "\n";
    } else {
        std::cout << "NIE\n";
    }

    return 0;
}