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;
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();
}
