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;
long long po(long long a, long long b) {
  long long x = 1, y = a;
  while (b > 0) {
    if (b % 2) {
      x = x * y;
      x %= 1000000007;
    }
    y = y * y;
    y %= 1000000007;
    b /= 2;
  }
  return x;
}
string mat[4];
int n;
void gen(int x, int y) {
  for (int i = 0; i < 4; i++) mat[i] = "";
  for (int i = 0; i < n; i++) {
    mat[0] += '.';
  }
  for (int i = 0; i < n; i++) {
    if (i > 0 && i <= x)
      mat[1] += '#';
    else
      mat[1] += '.';
  }
  for (int i = 0; i < n; i++) {
    if (i > 0 && i <= y)
      mat[2] += '#';
    else
      mat[2] += '.';
  }
  for (int i = 0; i < n; i++) {
    mat[3] += '.';
  }
  return;
}
const int mod1 = 1e9 + 7, mod2 = 1e9 + 9;
bool ok() {
  static long long dp[4][205];
  static long long dp1[4][205];
  dp[0][0] = 1ll;
  dp1[0][0] = 1ll;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      if (i == 0 && j == 0) continue;
      if (mat[i][j] == '#') {
        dp[i][j] = 0;
        dp1[i][j] = 0;
        continue;
      }
      dp[i][j] = 0;
      dp1[i][j] = 0;
      if (i > 0) {
        dp[i][j] += dp[i - 1][j];
        dp1[i][j] += dp1[i - 1][j];
      }
      if (j > 0) {
        dp[i][j] += dp[i][j - 1];
        dp1[i][j] += dp1[i][j - 1];
      }
      dp[i][j] %= mod1;
      dp1[i][j] %= mod2;
    }
  }
  long long x = dp[3][n - 1];
  long long y = dp1[3][n - 1];
  dp[3][0] = dp1[3][0] = 1ll;
  for (int i = 3; i >= 0; i--) {
    for (int j = 0; j < n; j++) {
      if (i == 3 && j == 0) continue;
      if (mat[i][j] == '#') {
        dp[i][j] = 0;
        dp1[i][j] = 0;
        continue;
      }
      dp[i][j] = 0;
      dp1[i][j] = 0;
      if (i < 3) {
        dp[i][j] += dp[i + 1][j];
        dp1[i][j] += dp1[i + 1][j];
      }
      if (j > 0) {
        dp[i][j] += dp[i][j - 1];
        dp1[i][j] += dp1[i][j - 1];
      }
      dp[i][j] %= mod1;
      dp1[i][j] %= mod2;
    }
  }
  return (dp[0][n - 1] == x && dp1[0][n - 1] == y);
}
int main() {
  if (0) {
    freopen("C:/Users/gold/Desktop/sublime IO/input.txt", "r", stdin);
    freopen("C:/Users/gold/Desktop/sublime IO/output.txt", "w", stdout);
  }
  int T = 1;
  while (T--) {
    int k;
    scanf("%d %d", &n, &k);
    if (k % 2 == 0) {
      puts("YES");
      for (int i = 0; i < n; i++) {
        printf(".");
      }
      puts("");
      for (int i = 0; i < n; i++) {
        if (i > 0 && i <= k / 2)
          printf("#");
        else
          printf(".");
      }
      puts("");
      for (int i = 0; i < n; i++) {
        if (i > 0 && i <= k / 2)
          printf("#");
        else
          printf(".");
      }
      puts("");
      for (int i = 0; i < n; i++) {
        printf(".");
      }
      puts("");
    } else {
      for (int i = 0; i <= k; i++) {
        if (i > n - 2 || (k - i) > n - 2) {
          continue;
        }
        gen(i, k - i);
        if (ok()) {
          puts("YES");
          for (int i = 0; i < 4; i++) {
            cout << mat[i] << endl;
          }
          exit(0);
        }
      }
      gen(0, 0);
      if (k >= n - 2) {
        for (int i = 1; i < n - 1; i++) {
          mat[1][i] = '#';
        }
        k -= (n - 2);
        assert(k < (n - 2));
        int extra = k / 2;
        int l1 = 1;
        int l2 = n - 2;
        for (int i = 0; i < extra; i++) {
          if (k > 0) {
            mat[2][l1] = '#';
            l1++;
            k--;
          }
          if (k > 0) {
            mat[2][l2] = '#';
            l2--;
            k--;
          }
        }
      }
      if (k > 0) {
        int mid = n / 2;
        int extra = k / 2;
        mat[2][mid] = '#';
        for (int i = 0; i < extra; i++) {
          mat[2][mid - 1 - i] = mat[2][mid + 1 + i] = '#';
        }
      }
      if (ok()) {
        puts("YES");
        for (int i = 0; i < 4; i++) {
          cout << mat[i] << endl;
        }
        exit(0);
      }
      puts("NO");
    }
  }
  return 0;
}
