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;
void center(vector<vector<char>> &arr, int row, int k, int n) {
  int mid = n / 2;
  arr[row][mid] = '#';
  k--;
  int i = mid - 1;
  int j = mid + 1;
  while (i >= 1 && j < n - 1 && k > 0) {
    arr[row][j] = '#';
    arr[row][i] = '#';
    i--;
    j++;
    k -= 2;
  }
}
void evenc(vector<vector<char>> &arr, int row, int k, int n) {
  int i = 1, j = n - 2;
  while (k > 0) {
    k -= 2;
    arr[row][i] = '#';
    arr[row][j] = '#';
    i++;
    j--;
  }
}
int main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n, k;
  cin >> n >> k;
  if (k > 2 * (n - 2))
    cout << "NO";
  else {
    cout << "YES" << endl;
    vector<vector<char>> arr(4, vector<char>(n, '.'));
    if (k % 2 == 0) {
      for (int i = 0; i < k / 2; i++) {
        arr[1][i + 1] = '#';
        arr[2][i + 1] = '#';
      }
    } else {
      if (k > n - 2) {
        for (int i = 1; i < n - 1; i++) arr[1][i] = '#';
        k -= n - 2;
        evenc(arr, 2, k, n);
      } else {
        center(arr, 1, k, n);
      }
    }
    for (int i = 0; i < 4; i++) {
      for (int j = 0; j < n; j++) cout << arr[i][j] << "";
      cout << endl;
    }
  }
  return 0;
}
