#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n = 0, m = 0, k = 0, i = 0, j = 0, p = 0, q = 0, x = 0, y = 0,
                z = 0, ans = 0, cnt = 0;
  string s;
  bool flag = false;
  cin >> n >> k;
  cout << "YES" << endl;
  char op[2][n - 2];
  for (i = 0; i < n - 2; i++) op[0][i] = '.', op[1][i] = '.';
  if (k % 2 == 0) {
    for (j = 0; j < (k / 2); j++) op[0][j] = '#', op[1][j] = '#';
  } else {
    if (k > n - 2) {
      for (i = 0; i < n - 2; i++) op[0][i] = '#';
      k = k - (n - 2);
      j = 0;
      for (i = 0; i < k; i += 2)
        op[1][j] = '#', op[1][n - 2 - j - 1] = '#', j++;
    } else {
      op[0][(n - 2) / 2] = '#';
      j = 0;
      k--;
      for (i = 0; i < k; i += 2)
        op[0][j] = '#', op[0][n - 2 - j - 1] = '#', j++;
    }
  }
  for (i = 0; i < 4; i++) {
    for (j = 0; j < n; j++) {
      if (i == 0 || j == 0 || i == 3 || j == n - 1)
        cout << '.';
      else
        cout << op[i - 1][j - 1];
    }
    cout << endl;
  }
  return 0;
}
