#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
stringstream output;
inline void eOP();
inline void solve() {
  output << "YES\n";
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < 4; ++i) {
    for (int j = 0; j < n; ++j) {
      if (i == 0 || i == 3 || j == 0 || j == n - 1) {
        output << ".";
        continue;
      }
      if (j == (n >> 1)) {
        if (i == 1) {
          if (k) {
            output << "#";
            continue;
          } else {
            output << ".";
            continue;
          }
        } else {
          if (k % 2 == 0 && k) {
            output << "#";
            continue;
          } else {
            output << ".";
            continue;
          }
        }
      }
      int x = min(j, n - 1 - j);
      if (x + (n / 2 - 1) * (i == 2) <= (k - 1) / 2) {
        output << "#";
        continue;
      } else {
        output << ".";
        continue;
      }
    }
    output << "\n";
  }
  output << flush;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  size_t t = 1;
  for (int i = 0; i < t; ++i) {
    solve();
  }
  eOP();
}
inline void eOP() {
  cout << output.str();
  output.str(string());
  exit(0);
}
