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;
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2")
int main() {
  int n, k;
  cin >> n >> k;
  cout << "YES" << endl;
  if (k % 2 == 0) {
    for (int i = 0; i < (4); ++i) {
      for (int j = 0; j < (n); ++j) {
        if (i == 0 || i == 3) {
          cout << '.';
        } else {
          if (j == 0 || j == n - 1) {
            cout << '.';
          } else if (j <= k / 2) {
            cout << '#';
          } else {
            cout << '.';
          }
        }
      }
      cout << endl;
    }
  } else if (k >= n - 2) {
    bool flag = false;
    for (int i = 0; i < (4); ++i) {
      if (i == 2) {
        int temp = k / 2;
        string a = ".";
        for (int j = 0; j < (temp); ++j) {
          a += '#';
        }
        for (int j = 0; j < (n - 2 - k); ++j) {
          a += '.';
        }
        for (int j = 0; j < (temp); ++j) {
          a += '#';
        }
        a += '.';
        cout << a;
      }
      for (int j = 0; j < (n); ++j) {
        if (i == 0 || i == 3) {
          cout << '.';
        } else if (i == 1) {
          if (j == 0 || j == n - 1) {
            cout << '.';
          } else if (k > 0) {
            cout << '#';
            k--;
          } else {
            cout << '.';
          }
        }
      }
      cout << endl;
    }
  } else {
    for (int i = 0; i < (n); ++i) {
      cout << '.';
    }
    cout << endl;
    for (int i = 0; i < ((n - k) / 2); ++i) {
      cout << '.';
    }
    for (int i = 0; i < (k); ++i) {
      cout << '#';
    }
    for (int i = 0; i < ((n - k) / 2); ++i) {
      cout << '.';
    }
    cout << endl;
    for (int i = 0; i < (n); ++i) {
      cout << '.';
    }
    cout << endl;
    for (int i = 0; i < (n); ++i) {
      cout << '.';
    }
    cout << endl;
  }
  return 0;
}
