docker_space/frontier_cs_3/solution_v7.cpp

#include <bits/stdc++.h>
using namespace std;

static int N;

static inline int readInt() {
    int c = getchar_unlocked();
    while (c != '-' && (c < '0' || c > '9')) {
        c = getchar_unlocked();
        if (c == EOF) return 0;
    }
    int sgn = 1;
    if (c == '-') { sgn = -1; c = getchar_unlocked(); }
    int x = 0;
    while (c >= '0' && c <= '9') { x = x*10+(c-'0'); c = getchar_unlocked(); }
    return x * sgn;
}

static char wbuf[1 << 23];
static int wpos = 0;
static void wflush() { if (wpos > 0) fwrite(wbuf, 1, wpos, stdout); wpos = 0; fflush(stdout); }
static void wchar(char c) { if (wpos >= (1<<23)-2) wflush(); wbuf[wpos++] = c; }
static void wint(long long x) {
    if (x < 0) { wchar('-'); x = -x; }
    if (x == 0) { wchar('0'); return; }
    char buf[20]; int len = 0;
    while (x > 0) { buf[len++] = '0'+(int)(x%10); x /= 10; }
    for (int i = len-1; i >= 0; i--) wchar(buf[i]);
}

static int resBuf[10000010];

static void doRound(const vector<int>& ops, int* res) {
    wint((int)ops.size());
    for (int x : ops) { wchar(' '); wint(x); }
    wchar('\n'); wflush();
    for (int i = 0; i < (int)ops.size(); i++) res[i] = readInt();
}

static void doRoundIgnore(const vector<int>& ops) {
    if (ops.empty()) return;
    doRound(ops, resBuf);
}

static mt19937 rng(42);

static void solve_small() {
    vector<int> ops;
    vector<pair<int,int>> pairs;
    for (int i = 1; i <= N; i++)
        for (int j = i+1; j <= N; j++) {
            ops.push_back(i); ops.push_back(j);
            ops.push_back(i); ops.push_back(j);
            pairs.push_back({i,j});
        }
    doRound(ops, resBuf);
    vector<vector<int>> adj(N+1);
    for (size_t k = 0; k < pairs.size(); k++)
        if (resBuf[4*k+1] == 1) {
            adj[pairs[k].first].push_back(pairs[k].second);
            adj[pairs[k].second].push_back(pairs[k].first);
        }
    vector<int> chain = {1};
    if (N > 1 && !adj[1].empty()) {
        chain.push_back(adj[1][0]);
        for (int i = 2; i < N; i++) {
            int last = chain.back(), prev = chain[chain.size()-2];
            for (int nb : adj[last])
                if (nb != prev) { chain.push_back(nb); break; }
        }
    }
    wint(-1);
    for (int v : chain) { wchar(' '); wint(v); }
    wchar('\n'); wflush();
}

// Build IS using batch approach with iteration limit
// Precondition: S is empty
// Postcondition: S = IS (returned)
static vector<int> buildIS(vector<int> nodes, int maxIters) {
    if (nodes.empty()) return {};
    shuffle(nodes.begin(), nodes.end(), rng);

    set<int> isSet;
    vector<int> IS;
    vector<int> candidates = nodes;

    for (int iter = 0; iter < maxIters && !candidates.empty(); iter++) {
        shuffle(candidates.begin(), candidates.end(), rng);

        // Toggle all candidates
        doRound(candidates, resBuf);
        int j = (int)candidates.size();
        for (int i = 0; i < (int)candidates.size(); i++) {
            if (resBuf[i] == 1) { j = i; break; }
        }

        for (int i = 0; i < j; i++) {
            IS.push_back(candidates[i]);
            isSet.insert(candidates[i]);
        }

        // Cleanup
        if (j < (int)candidates.size()) {
            vector<int> rem;
            for (int i = (int)candidates.size()-1; i >= j; i--)
                rem.push_back(candidates[i]);
            doRoundIgnore(rem);
        }
        if (j == (int)candidates.size()) break;

        // Probe to filter IS-adjacent candidates
        vector<int> remaining;
        for (int v : candidates) if (!isSet.count(v)) remaining.push_back(v);
        if (remaining.empty()) break;

        {
            vector<int> ops;
            ops.reserve(2 * remaining.size());
            for (int v : remaining) { ops.push_back(v); ops.push_back(v); }
            doRound(ops, resBuf);
        }
        candidates.clear();
        for (int i = 0; i < (int)remaining.size(); i++) {
            if (resBuf[2*i] == 0) candidates.push_back(remaining[i]);
        }
    }

    return IS;
}

// Phase 2: Combined sum+sq identification
// After calling: curLit reflects final IS configuration
static void identifyEdgesCombined(
    const vector<int>& IS, const vector<int>& nonIS,
    vector<array<int,2>>& adj, vector<int>& deg,
    vector<bool>& curLit
) {
    int m = (int)IS.size();
    int nm = (int)nonIS.size();
    if (m == 0 || nm == 0) return;

    int bits_sum = 0;
    { int v = 2*m; while (v > 0) { bits_sum++; v >>= 1; } }
    bits_sum = max(bits_sum, 1);

    int bits_sq = 0;
    { long long v = 2LL*m*m; while (v > 0) { bits_sq++; v >>= 1; } }
    bits_sq = max(bits_sq, 1);

    // Use random hash to replace sq, reducing bits needed
    // Hash: h_i = random in [0, 2*m)
    // We need sum (bits_sum bits) and hash_sum (bits_hash bits)
    // bits_hash = bits_sum + 1 (since hash_sum can be up to 4m)

    // Actually, let's use the sum+hash approach:
    // For each IS node i, label = i+1, hash = random in [0, H) where H = 2*m
    // bits for hash_sum = ceil(log2(2*H)) = ceil(log2(4m))
    // Combined rounds: max(bits_sum, bits_hash) = max(ceil(log2(2m)), ceil(log2(4m)))
    //   = ceil(log2(4m)) = bits_sum + 1

    // Compared to sum+sq combined: max(bits_sum, bits_sq) = bits_sq ≈ 2*bits_sum
    // Savings: bits_sq - (bits_sum+1) = bits_sum - 1 ≈ 16 rounds!

    // BUT: hash collision probability. For a given sum S, there are min(S-1, 2m-S) ≈ m/2 pairs.
    // Hash collision: probability that two different pairs with same sum have same hash_sum.
    // For pair (a,b): hash_sum = h_a + h_b.
    // For different pair (c,d) with c+d=a+b: hash_sum' = h_c + h_d.
    // P(hash_sum = hash_sum') = 1/H (approximately, for random h).
    // Number of "competitor" pairs per node: ~m/2.
    // P(any collision) per node ≈ m/(2H) = 1/4. Too high!

    // Need H >> m for low collision. H = m^2: bits_hash = 2*bits_sum. Same as sq.
    // H = m*k: collision prob ≈ 1/(2k). For k=100: prob=0.5%. bits_hash = bits_sum + 7.
    // Compared to sq: saves bits_sum - 8 ≈ 9 rounds for m=33K.

    // Let's try H = m * 256 (collision prob < 0.2%)
    // bits_hash = ceil(log2(2*m*256)) = ceil(log2(512*m)) = bits_sum + 9
    // Combined rounds: max(bits_sum, bits_sum+9) = bits_sum + 9
    // Original sq: bits_sq = ceil(log2(2*m^2)) = 2*bits_sum + 1
    // Savings: 2*bits_sum + 1 - (bits_sum + 9) = bits_sum - 8 ≈ 9 rounds for m=33K

    // For m=23K (100-iteration Phase 1): bits_sum=16, bits_sq=30, bits_hash=25
    // Savings: 30-25 = 5 rounds. Modest.

    // Let's stick with the standard sum+sq approach for correctness.

    vector<long long> labsq(m);
    for (int i = 0; i < m; i++) labsq[i] = (long long)(i+1)*(i+1);

    vector<long long> nsum(nm, 0), nsq(nm, 0);
    vector<int> carry_s(nm, 0), carry_q(nm, 0);
    int maxBits = max(bits_sum, bits_sq);

    for (int b = 0; b < maxBits; b++) {
        bool doSum = (b < bits_sum);
        bool doSq = (b < bits_sq);

        vector<int> ops;

        int sum_po1 = -1, sum_po2 = -1, sq_po1 = -1, sq_po2 = -1;

        if (doSum) {
            for (int i = 0; i < m; i++) {
                bool want = (((i+1)>>b)&1)==1;
                if (curLit[i] != want) { ops.push_back(IS[i]); curLit[i] = want; }
            }
            sum_po1 = (int)ops.size();
            for (int v : nonIS) { ops.push_back(v); ops.push_back(v); }
            for (int i = 0; i < m; i++) {
                bool want = (((i+1)>>b)&1)==0;
                if (curLit[i] != want) { ops.push_back(IS[i]); curLit[i] = want; }
            }
            sum_po2 = (int)ops.size();
            for (int v : nonIS) { ops.push_back(v); ops.push_back(v); }
        }

        if (doSq) {
            for (int i = 0; i < m; i++) {
                bool want = ((labsq[i]>>b)&1)==1;
                if (curLit[i] != want) { ops.push_back(IS[i]); curLit[i] = want; }
            }
            sq_po1 = (int)ops.size();
            for (int v : nonIS) { ops.push_back(v); ops.push_back(v); }
            for (int i = 0; i < m; i++) {
                bool want = ((labsq[i]>>b)&1)==0;
                if (curLit[i] != want) { ops.push_back(IS[i]); curLit[i] = want; }
            }
            sq_po2 = (int)ops.size();
            for (int v : nonIS) { ops.push_back(v); ops.push_back(v); }
        }

        doRound(ops, resBuf);

        if (doSum) {
            for (int j = 0; j < nm; j++) {
                int ho = resBuf[sum_po1+2*j];
                int hz = resBuf[sum_po2+2*j];
                int cnt = !ho ? 0 : !hz ? 2 : 1;
                int total = cnt + carry_s[j];
                if (total & 1) nsum[j] |= (1LL << b);
                carry_s[j] = total >> 1;
            }
        }
        if (doSq) {
            for (int j = 0; j < nm; j++) {
                int ho = resBuf[sq_po1+2*j], hz = resBuf[sq_po2+2*j];
                int cnt = !ho ? 0 : !hz ? 2 : 1;
                int total = cnt + carry_q[j];
                if (total & 1) nsq[j] |= (1LL << b);
                carry_q[j] = total >> 1;
            }
        }
    }
    for (int j = 0; j < nm; j++) {
        if (carry_s[j]) nsum[j] |= ((long long)carry_s[j] << bits_sum);
        if (carry_q[j]) nsq[j] |= ((long long)carry_q[j] << bits_sq);
    }

    auto addEdge = [&](int u, int v) {
        if (u == v || u < 1 || u > N || v < 1 || v > N) return;
        if (deg[u] >= 2 || deg[v] >= 2) return;
        for (int k = 0; k < deg[u]; k++) if (adj[u][k] == v) return;
        adj[u][deg[u]++] = v;
        adj[v][deg[v]++] = u;
    };

    for (int j = 0; j < nm; j++) {
        long long S1 = nsum[j], S2 = nsq[j];
        if (S1 == 0 && S2 == 0) continue;
        long long disc = 2*S2 - S1*S1;
        if (disc < 0) continue;
        long long d = (long long)round(sqrt((double)disc));
        while (d > 0 && d*d > disc) d--;
        while ((d+1)*(d+1) <= disc) d++;
        if (d*d != disc) continue;
        if ((S1+d)%2 != 0) continue;
        long long la = (S1+d)/2, lb = (S1-d)/2;
        if (la >= 1 && la <= m) addEdge(nonIS[j], IS[la-1]);
        if (lb >= 1 && lb <= m && lb != la) addEdge(nonIS[j], IS[lb-1]);
    }
}

static void solve_large() {
    vector<int> allNodes(N);
    iota(allNodes.begin(), allNodes.end(), 1);

    // Phase 1: Build IS with limited iterations
    vector<int> IS = buildIS(allNodes, 500);
    int m = (int)IS.size();

    vector<bool> inIS(N+1, false);
    for (int v : IS) inIS[v] = true;

    vector<int> nonIS;
    for (int v = 1; v <= N; v++) if (!inIS[v]) nonIS.push_back(v);
    int nm = (int)nonIS.size();

    // Phase 2: Identify edges (combined sum+sq)
    vector<array<int,2>> adj(N+1, {0,0});
    vector<int> deg(N+1, 0);
    vector<bool> curLit(m, true);
    identifyEdgesCombined(IS, nonIS, adj, deg, curLit);

    // Clear S
    {
        vector<int> clearOps;
        for (int i = 0; i < m; i++)
            if (curLit[i]) { clearOps.push_back(IS[i]); curLit[i] = false; }
        if (!clearOps.empty()) doRoundIgnore(clearOps);
    }

    // Phase 4: Handle remaining edges (deg<2 nonIS nodes)
    vector<int> deg1;
    for (int v : nonIS) if (deg[v] < 2) deg1.push_back(v);

    if (!deg1.empty()) {
        vector<int> IS2 = buildIS(deg1, 500);
        int m2 = (int)IS2.size();
        set<int> is2Set(IS2.begin(), IS2.end());
        vector<int> nonIS2;
        for (int v : deg1) if (!is2Set.count(v)) nonIS2.push_back(v);
        int nm2 = (int)nonIS2.size();

        if (m2 > 0 && nm2 > 0) {
            // Binary identification (each nonIS2 node has 1 IS2-neighbor)
            vector<bool> curLit2(m2, true);
            int bits2 = 0;
            { int v = m2; while (v > 0) { bits2++; v >>= 1; } }
            bits2 = max(bits2, 1);
            vector<int> nsum2(nm2, 0);

            for (int b = 0; b < bits2; b++) {
                vector<int> ops;
                ops.reserve(m2 + 2*nm2);
                for (int i = 0; i < m2; i++) {
                    bool want = (((i+1)>>b)&1)==1;
                    if (curLit2[i] != want) { ops.push_back(IS2[i]); curLit2[i] = want; }
                }
                int po = (int)ops.size();
                for (int v : nonIS2) { ops.push_back(v); ops.push_back(v); }
                doRound(ops, resBuf);
                for (int j = 0; j < nm2; j++)
                    if (resBuf[po+2*j]==1) nsum2[j] |= (1<<b);
            }

            auto addEdge = [&](int u, int v) {
                if (u == v || u < 1 || u > N || v < 1 || v > N) return;
                if (deg[u] >= 2 || deg[v] >= 2) return;
                for (int k = 0; k < deg[u]; k++) if (adj[u][k] == v) return;
                adj[u][deg[u]++] = v;
                adj[v][deg[v]++] = u;
            };

            for (int j = 0; j < nm2; j++) {
                int label = nsum2[j];
                if (label >= 1 && label <= m2) addEdge(nonIS2[j], IS2[label-1]);
            }
        }
    }

    // Traverse ring
    vector<int> order;
    order.reserve(N);
    int start = 1;
    for (int v = 1; v <= N; v++) if (deg[v] == 2) { start = v; break; }
    int prev = 0, cur = start;
    for (int i = 0; i < N; i++) {
        order.push_back(cur);
        int nxt = (adj[cur][0] != prev) ? adj[cur][0] : adj[cur][1];
        prev = cur; cur = nxt;
        if (cur == 0 || cur == start) break;
    }
    if ((int)order.size() != N) {
        order.clear();
        for (int v = 1; v <= N; v++) order.push_back(v);
    }
    wint(-1);
    for (int v : order) { wchar(' '); wint(v); }
    wchar('\n'); wflush();
}

int main() {
    int subtask = readInt();
    N = readInt();
    if (N <= 1) { wint(-1); wchar(' '); wint(1); wchar('\n'); wflush(); return 0; }
    if (N <= 1500) solve_small();
    else solve_large();
    return 0;
}