#include using namespace std; int n; long long k; // Flat memo array: memo[r*2001+c], -1 means not queried vector memo; int query_count = 0; long long do_query(int r, int c) { int key = r * 2001 + c; if (memo[key] != -1) return memo[key]; cout << "QUERY " << r << " " << c << "\n"; cout.flush(); long long v; cin >> v; memo[key] = v; query_count++; return v; } void done(long long ans) { cout << "DONE " << ans << "\n"; cout.flush(); exit(0); } // Staircase count: count elements <= val in full matrix // Returns count and fills boundary array // boundary[i] = number of elements in row i that are <= val // Uses at most O(n) NEW queries (staircase property), but with memoization could be 0 long long staircase_le(long long val, vector& boundary) { boundary.resize(n + 1); long long count = 0; int j = n; for (int i = 1; i <= n; i++) { while (j >= 1 && do_query(i, j) > val) j--; boundary[i] = j; count += j; } return count; } void solve() { long long total = (long long)n * n; // Heap for extreme k long long heap_k = min(k, total - k + 1); if (heap_k + n <= 24000) { if (k <= total - k + 1) { priority_queue, vector>, greater<>> pq; vector> vis(n + 1, vector(n + 1, false)); pq.emplace(do_query(1, 1), 1, 1); vis[1][1] = true; long long result = -1; for (long long i = 0; i < k; i++) { auto [v, r, c] = pq.top(); pq.pop(); result = v; if (r + 1 <= n && !vis[r + 1][c]) { vis[r + 1][c] = true; pq.emplace(do_query(r + 1, c), r + 1, c); } if (c + 1 <= n && !vis[r][c + 1]) { vis[r][c + 1] = true; pq.emplace(do_query(r, c + 1), r, c + 1); } } done(result); } else { long long kk = total - k + 1; priority_queue> pq; vector> vis(n + 1, vector(n + 1, false)); pq.emplace(do_query(n, n), n, n); vis[n][n] = true; long long result = -1; for (long long i = 0; i < kk; i++) { auto [v, r, c] = pq.top(); pq.pop(); result = v; if (r - 1 >= 1 && !vis[r - 1][c]) { vis[r - 1][c] = true; pq.emplace(do_query(r - 1, c), r - 1, c); } if (c - 1 >= 1 && !vis[r][c - 1]) { vis[r][c - 1] = true; pq.emplace(do_query(r, c - 1), r, c - 1); } } done(result); } } // Quickselect approach: walk only active rows, use weighted pivot vector L(n + 1, 1), R(n + 1, n); long long k_rem = k; for (int iter = 0; iter < 100; iter++) { vector active; long long total_cand = 0; for (int i = 1; i <= n; i++) { if (L[i] <= R[i]) { active.push_back(i); total_cand += R[i] - L[i] + 1; } } int na = active.size(); if (total_cand == 0) break; if (total_cand == 1) { for (int i : active) done(do_query(i, L[i])); break; } // Heap fallback long long budget = 49500 - query_count; if (k_rem + na <= budget) { priority_queue, vector>, greater<>> pq; for (int i : active) pq.emplace(do_query(i, L[i]), i, L[i]); for (long long t = 1; t < k_rem; t++) { auto [v, r, c] = pq.top(); pq.pop(); if (c + 1 <= R[r]) pq.emplace(do_query(r, c + 1), r, c + 1); } done(get<0>(pq.top())); } long long rev_k = total_cand - k_rem + 1; if (rev_k + na <= budget) { priority_queue> pq; for (int i : active) pq.emplace(do_query(i, R[i]), i, R[i]); for (long long t = 1; t < rev_k; t++) { auto [v, r, c] = pq.top(); pq.pop(); if (c - 1 >= L[r]) pq.emplace(do_query(r, c - 1), r, c - 1); } done(get<0>(pq.top())); } // Pick pivot from quantiles of active rows // Query at k_rem/total_cand fraction within each row's range // This targets the expected rank better than midpoints vector pvals; double target_frac = (double)(k_rem - 0.5) / total_cand; for (int i : active) { int width = R[i] - L[i] + 1; int col = L[i] + (int)(target_frac * (width - 1)); col = max(L[i], min(R[i], col)); pvals.push_back(do_query(i, col)); } sort(pvals.begin(), pvals.end()); // Take median of these values long long pivot = pvals[na / 2]; // Staircase for <= over active rows only vector p_le(n + 1, 0), p_lt(n + 1, 0); { int j = n; for (int i : active) { j = min(j, R[i]); while (j >= L[i] && do_query(i, j) > pivot) j--; p_le[i] = j; } } { int j = n; for (int i : active) { j = min(j, R[i]); while (j >= L[i] && do_query(i, j) >= pivot) j--; p_lt[i] = j; } } long long cle = 0, clt = 0; for (int i : active) { int rl = min(p_le[i], R[i]); if (rl >= L[i]) cle += rl - L[i] + 1; int rt = min(p_lt[i], R[i]); if (rt >= L[i]) clt += rt - L[i] + 1; } if (k_rem <= clt) { for (int i : active) R[i] = min(R[i], p_lt[i]); } else if (k_rem <= cle) { done(pivot); } else { k_rem -= cle; for (int i : active) L[i] = max(L[i], p_le[i] + 1); } } } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cin >> n >> k; memo.assign(2002 * 2002, -1); solve(); return 0; }