#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("no-stack-protector")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
using namespace std;
void seriy() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
char res[4][100];
long long n, k;
void out() {
  for (long long i = 0; i < 4; i++) {
    for (long long j = 0; j < n; j++) {
      cout << res[i][j];
    }
    cout << endl;
  }
}
signed main() {
  seriy();
  cin >> n >> k;
  long long l = k;
  cout << "YES\n";
  for (long long i = 0; i < 4; i++) {
    for (long long j = 0; j < n; j++) {
      res[i][j] = '.';
      if (k == 2 * (n - 2) && (i == 1 || i == 2) && j > 0 && j < n - 1) {
        res[i][j] = '#';
      }
    }
  }
  if (k == 2 * (n - 2)) {
    out();
    return 0;
  }
  for (long long i = 1; i < n / 2; i++) {
    if (l <= 0) {
      out();
      return 0;
    }
    if (l == 1) {
      res[1][n / 2] = '#';
      out();
      return 0;
    }
    res[1][i] = '#';
    res[1][n - i - 1] = '#';
    l -= 2;
  }
  for (long long i = 1; i < n / 2; i++) {
    if (l <= 0) {
      out();
      return 0;
    }
    if (l == 1) {
      res[1][n / 2] = '#';
      out();
      return 0;
    }
    res[2][i] = '#';
    res[2][n - i - 1] = '#';
    l -= 2;
  }
  if (l <= 0) {
    out();
    return 0;
  }
  if (l == 1) {
    res[1][n / 2] = '#';
    out();
    return 0;
  }
  return 0;
}
