#include "island.h"
#include "bits/stdc++.h"
using namespace std;
template<typename T>
using vec = vector<T>;
struct DSU {
public:
    DSU() : _n(0) {}
    explicit DSU(int n) : _n(n), parent_or_size(n, -1) {}
    int unite(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }
    bool one(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }
    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }
    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }
    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
                std::remove_if(result.begin(), result.end(),
                               [&](const std::vector<int> &v) { return v.empty(); }),
                result.end());
        return result;
    }
private:
    int _n;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;
};
void solve(int N, int L) {
    map<pair<int, int>, int> mp;
    auto ask = [&](int a, int b) {
        if (mp.contains({a, b})) return mp[{a, b}];
        return mp[{a, b}] = query(a, b);
    };
    vec<vec<int>> g(N + 1);
    DSU dsu(N + 1);
    for (int i = 1; i <= N; i++) {
        int k = 1;
        for (auto u: g[i]) {
            if (u < i) k++;
        }
        while (k < N) {
            int v = ask(i, k);
            if (dsu.one(i, v)) break;
            if (v < i) break;
            if (k > 1) {
                int cnt = 1;
                for (auto u: g[v]) {
                    if (u < i) cnt++;
                }
                if (ask(v, cnt) != i) break;
            }
            g[v].push_back(i);
            dsu.unite(i, v);
            g[i].push_back(v);
            answer(i, v);
            k++;
        }
    }
}
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