#include <bits/stdc++.h>

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);
    for(int i = 0; i < ans; i++) {
      for(int j = 0; j < ans; j++) {
        if(v[i][j]) cout << "#";
        else cout << ".";
      }
      cout << endl;
    }
    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;
  }
}