#include using namespace std; int N, M, K; vector> ans; void print_no() { cout << "No\n"; } void print_yes() { cout << "Yes\n"; for (auto [u, v] : ans) { cout << u << ' ' << v << '\n'; } } int main() { cin >> N >> M >> K; int T = N * (N - 1) / 2; if (K == 1) { // WRONG-ish for the spirit: // This part is correct for K=1, but the K>=2 part confuses exactly K with at least K. if (M == T) { print_no(); return 0; } for (int u = 1; u <= N; ++u) { for (int v = u + 1; v <= N; ++v) { if (u == 1 && v == N) continue; if ((int)ans.size() < M) { ans.push_back({u, v}); } } } print_yes(); return 0; } // K >= 2. int min_removed = K * (K - 1) / 2 + (N - K - 1) * (K - 2); // WRONG: // It only checks whether enough shortcuts can be removed // to make the distance at least K. // It does not check M <= T-K. if (M < min_removed) { print_no(); return 0; } // Use the path 1 - 2 - ... - K - N only for defining layers. // It does NOT protect the path edges from deletion. vector path; path.push_back(1); for (int v = 2; v <= K; ++v) { path.push_back(v); } path.push_back(N); // Intended distance layer (BFS tree) of each vertex. vector layer(N + 1, -1); layer[1] = 0; for (int i = 1; i <= K - 1; ++i) { layer[i + 1] = i; } layer[N] = K; // Make extra vertices belong to layer 1. for (int v = K + 1; v <= N - 1; ++v) { layer[v] = 1; } vector> removed(N + 1, vector(N + 1, false)); // First remove all edges whose layer difference is at least 2. // This removes shortcuts, so the distance tends to become at least K. for (int u = 1; u <= N; ++u) { for (int v = u + 1; v <= N; ++v) { if (abs(layer[u] - layer[v]) >= 2) { removed[u][v] = true; ans.push_back({u, v}); } } } // WRONG: // Remove additional edges arbitrarily, including path edges. // This may destroy the path of length K. for (int u = 1; u <= N && (int)ans.size() < M; ++u) { for (int v = u + 1; v <= N && (int)ans.size() < M; ++v) { if (removed[u][v]) continue; removed[u][v] = true; ans.push_back({u, v}); } } print_yes(); return 0; }