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 n, k, kk, m;
int a[105];
int main() {
  cin >> n >> k;
  m = n / 2;
  if (2 * (n - 2) < k)
    cout << "NO\n";
  else if (k % 2 == 0) {
    kk = k / 2;
    cout << "YES\n";
    for (int i = 0; i < n; i++) cout << ".";
    cout << "\n.";
    for (int i = 1; i < n - 1; i++) {
      if (kk > 0)
        cout << "#";
      else
        cout << ".";
      kk--;
    }
    cout << ".\n.";
    kk = k / 2;
    for (int i = 1; i < n - 1; i++) {
      if (kk > 0)
        cout << "#";
      else
        cout << ".";
      kk--;
    }
    cout << ".\n";
    for (int i = 0; i < n; i++) cout << ".";
    cout << "\n";
  } else {
    cout << "YES\n";
    for (int i = 0; i < n; i++) cout << ".";
    cout << "\n.";
    if (k >= n - 2) {
      for (int i = 1; i < n - 1; i++) cout << "#";
      cout << ".\n.";
      if (k == n - 2) {
        for (int i = 1; i < n; i++) cout << ".";
        cout << "\n";
      } else {
        k -= (n - 2);
        for (int i = 1; i < m; i++)
          if (k >= 2) a[i] = 1, a[n - i - 1] = 1, k -= 2;
        for (int i = 1; i < n; i++) {
          if (a[i] == 1)
            cout << "#";
          else
            cout << ".";
        }
        cout << "\n";
      }
      for (int i = 0; i < n; i++) cout << ".";
    } else {
      for (int i = 1; i < m; i++)
        if (k >= 2) a[i] = 1, a[n - i - 1] = 1, k -= 2;
      if (k == 1) a[m] = 1;
      for (int i = 1; i < n; i++) {
        if (a[i] == 1)
          cout << "#";
        else
          cout << ".";
      }
      cout << "\n";
      for (int i = 0; i < n; i++) cout << ".";
      cout << "\n";
      for (int i = 0; i < n; i++) cout << ".";
    }
  }
}
