#include <bits/stdc++.h>
using namespace std;
struct city_t : array<bitset<99>, 4> {
  int n, k, m, p;
  city_t() { cin >> n >> k, m = n / 2, p = n - 2; }
  void hotel(int i, int j) {
    if (!(*this)[i][j] && k > 0) (*this)[i][j] = true, k--;
  }
  void solve() {
    if (k % 2) hotel(1, m);
    for (int i = 1; i < 3 && k > 0; i++)
      for (int u = 1, v = p; v > u && k > 0; u++, v--) hotel(i, u), hotel(i, v);
    hotel(1, m), hotel(2, m);
  }
  void write() {
    cout << "YES";
    for (int i = 0; i < 4; i++) {
      cout << '\n';
      for (int j = 0; j < n; j++)
        if ((*this)[i][j])
          cout << '#';
        else
          cout << '.';
    }
  }
};
int main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
  city_t city;
  city.solve(), city.write();
}
