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() {
  int n, k;
  cin >> n >> k;
  int a[n];
  int col[256];
  char was[256];
  for (int i = 0; i < n; ++i) cin >> a[i];
  for (int i = 0; i < 255; ++i) {
    col[i] = -1;
    was[i] = false;
  }
  for (int i = 0; i < n; ++i) {
    int q = -1;
    for (int j = a[i]; j > max(a[i] - k, -1); --j) {
      if (col[j] != -1 && was[j]) {
        q = j + 1;
        break;
      }
    }
    if (q == -1) q = max(a[i] - k, -1) + 1;
    for (int j = q; j < q + k; ++j) col[j] = q;
    cout << col[a[i]] << " ";
    was[a[i]] = true;
  }
}
int main() {
  int n, k;
  cin >> n >> k;
  if (k % 2 == 0) {
    cout << "YES\n";
    for (int i = 0; i < n; ++i) cout << ".";
    cout << "\n";
    cout << ".";
    for (int i = 0; i < k / 2; ++i) cout << "#";
    for (int i = 0; i < n - k / 2 - 1; ++i) cout << ".";
    cout << "\n";
    cout << ".";
    for (int i = 0; i < k / 2; ++i) cout << "#";
    for (int i = 0; i < n - k / 2 - 1; ++i) cout << ".";
    cout << "\n";
    for (int i = 0; i < n; ++i) cout << ".";
    cout << "\n";
  } else if (k == 3) {
    cout << "YES\n";
    for (int i = 0; i < n; ++i) cout << ".";
    cout << "\n";
    cout << ".#.#";
    for (int i = 0; i < n - 4; ++i) cout << ".";
    cout << "\n";
    cout << "...#";
    for (int i = 0; i < n - 4; ++i) cout << ".";
    cout << "\n";
    for (int i = 0; i < n; ++i) cout << ".";
    cout << "\n";
  } else if (k == 1) {
    cout << "YES\n";
    for (int i = 0; i < n; ++i) cout << ".";
    cout << "\n";
    for (int i = 0; i < n / 2; ++i) cout << ".";
    cout << "#";
    for (int i = 0; i < n / 2; ++i) cout << ".";
    cout << "\n";
    for (int i = 0; i < n; ++i) cout << ".";
    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";
    cout << ".";
    int k1 = min(k - 2, n - 2);
    k = k - k1;
    for (int i = 0; i < k1; ++i) cout << "#";
    for (int i = 0; i < n - k1 - 1; ++i) cout << ".";
    cout << "\n";
    cout << ".";
    for (int i = 0; i < k - 1; ++i) cout << "#";
    for (int i = 0; i < k1 - k; ++i) cout << ".";
    cout << "#";
    for (int i = 0; i < n - k1 - 1; ++i) cout << ".";
    cout << "\n";
    for (int i = 0; i < n; ++i) cout << ".";
    cout << "\n";
  }
}
