Problem: You are given two integers A and B.

Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:

* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.



It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.

Constraints

* 1 \leq A \leq 500
* 1 \leq B \leq 500

Input

Input is given from Standard Input in the following format:


A B


Output

Output should be in the following format:

* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.

Examples

Input

2 3


Output

3 3
##.
..#
#.#


Input

7 8


Output

3 5
.#.#
.#.#.
.#.#


Input

1 1


Output

4 2
..
.


Input

3 14


Output

8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
 
 
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
 
public class Main{ 
 
 
    static long mod=1000000007;
    static int dx[]={1,-1,0,0};
    static int dy[]={0,0,1,-1};
    // static int dx[]={1,-1,0,0,1,1,-1,-1};
    // static int dy[]={0,0,1,-1,1,-1,1,-1};
    // PriorityQueue<Integer> que = new PriorityQueue<Integer>(); 
    //HashMap<Integer,Integer> map = new HashMap<Integer,Integer>();
        // ArrayList<Integer> lis = new ArrayList<Integer>();
    // ArrayList<Integer> map[]=new ArrayList[26];
    static HashMap<Integer,Long> map = new HashMap<Integer,Long>();

    public  static void main(String[] args)   throws Exception, IOException{
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        // int n=sc.nextInt();
        // long n=sc.nextLong();
        // char c[][] = new char[h][w];
        // long a[] = new long [n];
        // char c[]=sc.nextString().toCharArray();
        // for(int i=0; i<n; i++) {a[i]=sc.nextInt();}
        // int n=sc.nextInt();
        int a=sc.nextInt(),b=sc.nextInt();
        int d[][] = new int[100][100];
        int c=0,mx=max(a,b),min=min(a,b);
        lp:for (int i=0;i<100; i+=4) {
            for (int t=0;t<100; t+=4) {
                d[i][t]=1;d[i][t+1]=1;d[i][t+2]=1;
                d[i+1][t]=1;d[i+1][t+1]=1;d[i+1][t+2]=1;
                d[i+2][t]=1;d[i+2][t+1]=1;d[i+2][t+2]=1;
                c++; if(c==mx)break lp;
            }
        }
        c=0;
        if(min>1)
        lp:for (int i=1;i<100; i+=4) {
                for (int t=1;t<100; t+=4) {
                    d[i][t]=0;
                    c++; if(c==min-1)break lp;
            }
        }
        // for (int i=0;i<99; i++)db(d[i]);

        out.println("100 100");
        for (int i=0;i<100; i++){ String s="";
            for (int t=0;t<100; t++){
                if(a<=b)s=s+( d[i][t]<1? ".":"#" );
                else s=s+( d[i][t]<1? "#":"." );
            }
            out.println(s);
        }

        
        // out.println(ans);
        out.flush();
    }

    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }
     
    static boolean validpos(int x,int y,int r, int c){
        return x<r && 0<=x && y<c && 0<=y;
    }
     
    static boolean bit(long x,int k){
        // weather k-th bit (from right) be one or zero
        return  ( 0 < ( (x>>k) & 1 )  )  ? true:false;
    }    
}

class XY {
    int x,y,d;
    XY(int x, int y, int d) {
        this.x=x;
        this.y=y;
        this.d=d;
    } 
}
 
class P implements Comparable<P>{
    int x,y;
    P(int x, int y) {
        this.x=x;
        this.y=y;
    } 
      
    public int compareTo(P p){
        return -x + p.x;//des
    } 
}
 
class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}