#include <bits/stdc++.h>
using namespace std;
int pwr(int base, int p) {
  int ans = 1;
  while (p) {
    if (p & 1) ans = (ans * base) % 1000000007;
    base = (base * base) % 1000000007;
    p /= 2;
  }
  return ans;
}
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int powr(int base, int p) {
  int ans = 1;
  while (p) {
    if (p & 1) ans = (ans * base);
    base = (base * base);
    p /= 2;
  }
  return ans;
}
int pre[200005];
int search(int l, int h, int val2) {
  int ans1 = -1;
  while (l <= h) {
    int m = (l + h) / 2;
    if (pre[m] > val2) {
      ans1 = m;
      h = m - 1;
    } else
      l = m + 1;
  }
  return ans1;
}
struct node {
  int x, y, i;
};
bool comp(node a, node b) { return a.y > b.y; }
vector<int> g[200005];
int main() {
  int n, k;
  scanf("%d", &n);
  scanf("%d", &k);
  char s[4][n];
  cout << "YES" << endl;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      s[i][j] = 'a';
    }
  }
  for (int i = 1; i <= 2; i++) {
    for (int j = 1; j < n / 2; j++) {
      if (k >= 2) {
        s[i][j] = '#';
        s[i][n - j - 1] = '#';
        k -= 2;
      } else
        break;
    }
  }
  if (k == 1) {
    s[1][n / 2] = '#';
  }
  if (k == 2) {
    s[1][n / 2] = '#';
    s[2][n / 2] = '#';
  }
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      if (s[i][j] == 'a') s[i][j] = '.';
      cout << s[i][j];
    }
    cout << endl;
  }
}
