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
.....
.###.
.....
.....
import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    private final static long mod = 1000000007;

    private static void printArr2(long arr[][]) {

        int i, j, n = arr.length, m = arr[0].length;
        for (i = 0; i < n; i++) {
            for (j = 0; j < m; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }
    }

    private static void printArr(int arr[][]) {
        int i, j, n = arr.length, m = arr[0].length;
        for (i = 0; i < n; i++) {
            for (j = 0; j < m; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }
    }

    private static long power(long x, long y) {
        long temp;
        if (y == 0)
            return 1;
        temp = power(x, y / 2);
        temp = (temp * temp) % mod;
        if (y % 2 == 0)
            return temp;
        else
            return ((x % mod) * temp) % mod;
    }


    private static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    private static class Obj{
        int len;
        int parent;
        int idx;

        public Obj(int len, int parent, int idx) {
            this.len = len;
            this.parent = parent;
            this.idx = idx;
        }
    }

    public static void main(String[] args) throws IOException {
        FastReader in = new FastReader();
        FastWriter out = new FastWriter();
        int t, i, j, k, w, r, x, y, l=0, n, m=0;
        long ans = 0;
        //for (t = in.nextInt(); t > 0; t--)
        {
            n=in.nextInt();
            k=in.nextInt();
            if(k%2==0){
                out.println("YES");
                out.printCharN('.',n);
                out.println();
                out.print(".");
                out.printCharN('#',k/2);
                out.printCharN('.',n-k/2-1);
                out.println();
                out.print(".");
                out.printCharN('#',k/2);
                out.printCharN('.',n-k/2-1);
                out.println();
                out.printCharN('.',n);
                out.println();
            }
            else{
                if(k<n){
                    out.println("YES");
                    out.printCharN('.',n);
                    out.println();
                    out.printCharN('.',(n-k)/2);
                    out.printCharN('#',k);
                    out.printCharN('.',(n-k)/2);
                    out.println();
                    out.printCharN('.',n);
                    out.println();
                    out.printCharN('.',n);
                    out.println();
                }
                else{
                    if(k>4){
                        k++;
                        out.println("YES");
                        out.printCharN('.',n);
                        out.println();
                        out.print(".");
                        out.printCharN('#',k/2);
                        out.printCharN('.',n-k/2-1);
                        out.println();
                        out.print(".#.");

                        out.printCharN('#',k/2-2);
                        out.printCharN('.',n-k/2-1);
                        out.println();
                        out.printCharN('.',n);
                        out.println();
                    }
                    else
                    out.println("NO");
                }
            }
            out.println();
        }

    }

    static class FastReader {
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private StringTokenizer st;

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] nextIntArr(int n) {
            int []arr=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=nextInt();
            }
            return arr;
        }

        long[] nextLongArr(int n) {
            long []arr=new long[n];
            for(int i=0;i<n;i++){
                arr[i]=nextLong();
            }
            return arr;
        }

    }

    static class FastWriter {
        BufferedWriter bw;
        List<String> list = new ArrayList<>();
        Set<String> set = new HashSet<>();

        FastWriter() {
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        <T> void print(T obj) throws IOException {
            bw.write(obj.toString());
            bw.flush();
        }

        void println() throws IOException {
            print("\n");
        }

        <T> void println(T obj) throws IOException {
            print(obj.toString() + "\n");
        }

        <T> void printArrLn(T[] arr) throws IOException{
            for(int i=0;i<arr.length;i++){
                print(arr[i]+" ");
            }
            println();
        }

        void printCharN(char c, int n) throws IOException {
            for(int i=0;i<n;i++){
                print(c);
            }
        }
    }
}
