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;
inline int setBit(int N, int pos) { return N = N | (1 << pos); }
inline int resetBit(int N, int pos) { return N = N & ~(1 << pos); }
inline bool checkBit(int N, int pos) { return (bool)(N & (1 << pos)); }
string s;
char grid[10][110];
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) grid[i][j] = '.';
    grid[i][n] = 0;
  }
  for (int i = 1, j = n - 2; i < n / 2; i++, j--) {
    if (k <= 1) break;
    for (int row = 1; row <= 2; row++) {
      if (k <= 1) break;
      grid[row][i] = grid[row][j] = '#';
      k -= 2;
    }
  }
  for (int i = 1, j = n / 2; i <= 2 && k; i++) {
    k--;
    grid[i][j] = '#';
  }
  puts("YES");
  for (int i = 0; i < 4; i++) puts(grid[i]);
  return 0;
}
