The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).

The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.

A person can move from one cell to another if those cells are not occupied by hotels and share a side.

Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?

Input

The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.

Output

Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".

If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.

Examples

Input

7 2


Output

YES
.......
.#.....
.#.....
.......


Input

5 3


Output

YES
.....
.###.
.....
.....
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0), cout.tie();
  int n, k;
  cin >> n >> k;
  cout << "YES\n";
  if (k & 1) {
    if (k <= n - 2) {
      for (int i = 1; i <= n; ++i) cout << '.';
      cout << '\n';
      for (int i = 1; i <= n; ++i)
        if (i == (n + 1) / 2)
          cout << '#';
        else if (abs(i - (n + 1) / 2) <= (k - 1) >> 1)
          cout << '#';
        else
          cout << '.';
      cout << '\n';
      for (int i = 1; i <= n; ++i) cout << '.';
      cout << '\n';
      for (int i = 1; i <= n; ++i) cout << '.';
    } else {
      for (int i = 1; i <= n; ++i) cout << '.';
      cout << '\n';
      for (int i = 1; i <= n; ++i)
        if (i == 1 || i == n)
          cout << '.';
        else
          cout << '#', --k;
      cout << '\n';
      k -= 2;
      fprintf(stderr,
              "("
              "k"
              ") = ("
              "%d"
              ")\n",
              k);
      for (int i = 1; i <= n; ++i) {
        if (i == 1 || i == n)
          cout << '.';
        else if (i == 2 || i == n - 1)
          cout << '#';
        else if (k > 0)
          cout << '#', --k;
        else
          cout << '.';
      }
      cout << '\n';
      for (int i = 1; i <= n; ++i) cout << '.';
    }
  } else {
    for (int i = 1; i <= 4; ++i, cout << '\n') {
      if (i == 1 || i == 4)
        for (int j = 1; j <= n; ++j) cout << '.';
      else {
        cout << '.';
        for (int j = 2; j <= n; ++j)
          if (j - 1 <= k >> 1)
            cout << '#';
          else
            cout << '.';
      }
    }
  }
  return 0;
}
