#include using namespace std; using int64 = long long; const int mod = 998244353; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } int main() { int N, K; cin >> N >> K; if(N < 50) { auto dp = make_v< int >(N + 1, N + 1, N + 1); fill_v(dp, -1); auto rec = MFP([&](auto rec, int x, int y, int zan) -> int { if(zan <= 0) return max(x, y); if(~dp[x][y][zan]) return dp[x][y][zan]; int ret = inf; for(int i = 1; i <= min(K, N); i++) { for(int j = 1; j <= K; j++) { chmin(ret, rec(x + i, y + j, zan - i * j)); } } return dp[x][y][zan] = ret; }); auto ans = rec(0, 0, N); int v[1500][1500] = {{}}; auto rec2 = MFP([&](auto rec2, int x, int y, int zan) -> void { if(zan <= 0) return; for(int i = 1; i <= min(K, N); i++) { for(int j = 1; j <= K; j++) { if(rec(x + i, y + j, zan - i * j) == dp[x][y][zan]) { for(int k = 0; k < i; k++) { for(int l = 0; l < j; l++) { if(N > 0) { --N; v[x + k][y + l] = true; } } } rec2(x + i, y + j, zan - i * j); return; } } } }); cout << ans << endl; rec2(0, 0, N); int put = 0; for(int i = 0; i < ans; i++) { for(int j = 0; j < ans; j++) { if(v[i][j]) { cout << "#"; ++put; } else { cout << "."; } } cout << endl; } assert(put == N); return 0; } auto dp = make_v< int >(N + 1); auto pre = make_v< int >(N + 1); for(int i = 0; i <= N; i++) { for(int j = 1; i + j <= N && j <= K; j++) { if(chmax(dp[i + j], dp[i] + j * j)) { pre[i + j] = j; } } } int last = inf; for(int i = N; i >= 0; i--) { if(dp[i] >= N) last = i; } cout << last << endl; int cur = last; int v[1500][1500] = {{}}; int used = 0; while(cur > 0) { int now = pre[cur]; for(int i = 0; i < now; i++) { for(int j = 0; j < now; j++) { if(N > 0) { if(used + i >= last || used + j >= last) { continue; } v[used + i][used + j] = true; --N; } } } used += now; cur -= now; } for(int i = 0; i < last; i++) { for(int j = 0; j < last; j++) cout << ".#"[v[i][j]]; cout << endl; } }