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.*;

	
public class Main {
    
    static class Graph0n {
        private ArrayList<Node0n> dt = new ArrayList<>();
        Graph0n(int sz){for(int i=0; i<sz; i++){Node0n node1 = new Node0n();dt.add(node1);}}
        public void add(int vn, int val){   dt.get(vn).add(val);                    }
        public void add2(int vn, int val){  dt.get(vn).add(val);dt.get(val).add(vn);}
        public int get(int vn, int index){      return dt.get(vn).get(index);       }
        public ArrayList<Integer> get(int vn){  return dt.get(vn).getAll();         }
        public int sizeOf(int vn){              return dt.get(vn).size();           }
        public void clear(){    for(int i=0; i<dt.size(); i++){ dt.get(i).clear();  }   }
    }
    static class Node0n {   //重みなし無向・有向グラフの頂点
        private ArrayList<Integer> next_vs = new ArrayList<>();
        public void add(int val){               next_vs.add(val);       }
        public int get(int ad){                 return next_vs.get(ad); }
        public ArrayList<Integer> getAll(){     return next_vs;         }
        public int size(){                      return next_vs.size();  }
        public void clear(){                    next_vs.clear();        }
    }

    static class Edge {
        int from=-1, v2=-1;     long weight;
        public Edge(int vn, long w){
            this.v2 = vn;
            this.weight = w;
        }
        public Edge(int cm, int vn, long w){
            this.from = cm;
            this.v2 = vn;
            this.weight = w;
        }
    }
    static class Edge2 {
        int v2;     long cost1,cost2;
        public Edge2(int vn, long w1, long w2){
            this.v2 = vn;
            this.cost1 = w1;
            this.cost2 = w2;
        }
    }

    static class Comparator_Edge implements Comparator<Edge>{       //今は大きいのが前に出てくる
        public int compare(Edge a, Edge b){
            if(a.weight>b.weight) return -1;
            else if(a.weight<b.weight) return 1;
            else return a.v2-b.v2;
        }
    }
    
    static class Vector {
        int x,y;
        public Vector(int sx, int sy){
            this.x=sx;
            this.y=sy;
        }
    }
    
    //私が好きなアルゴリズム：：累積和・UF木
    //PriorityQueueは拡張for文で出すとsortされてない順番で出てくるよ
    //longのbit演算は1L<<posに注意
    
	public static void main(String[] args) throws Exception {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
	    
	    int wn = sc.nexI();
	    int bn = sc.nexI();
	    
	    wn--;
	    bn--;
	    
	    out.println("50 100");
	    int done = 0;
	    for(int i=0; i<25; i++){
	        for(int j=0; j<100; j++){
	            if((i%2==0)&&(j%2==0)&&(done<wn)){
	                out.print('.');
	                done++;
	            }else{
	                out.print('#');
	            }
	        }
	        out.println();
	    }
	    done = 0;
	    for(int i=0; i<25; i++){
	        for(int j=0; j<100; j++){
	            if((i%2==1)&&(j%2==0)&&(done<bn)){
	                out.print('#');
	                done++;
	            }else{
	                out.print('.');
	            }
	        }
	        out.println();
	    }
	    
	    out.flush();
	}
	
	
	private static List<Edge> factorizationP(int n){   //<指数,素数>
	    List<Edge> ans = new ArrayList<>();
	    
	    int quotient = n;
	    int devider = 2;
	    int exponent = 0;
	    
	    while(quotient%devider == 0){
	        quotient /= devider;
	        exponent++;
	    }
	    if(exponent>0) ans.add(new Edge(exponent, devider));
	    
	    devider = 3;    exponent = 0;
	    while(quotient%devider == 0){
	        quotient /= devider;
	        exponent++;
	    }
	    if(exponent>0) ans.add(new Edge(exponent, devider));
	    
	    devider=1;
	    while(devider <= Math.sqrt(n)){
	        devider+=4; exponent=0;
    	    while(quotient%devider == 0){
    	        quotient /= devider;
    	        exponent++;
    	    }
    	    if(exponent>0) ans.add(new Edge(exponent, devider));
    	    
	        devider+=2; exponent=0;
    	    while(quotient%devider == 0){
    	        quotient /= devider;
    	        exponent++;
    	    }
    	    if(exponent>0) ans.add(new Edge(exponent, devider));
	    }
	    if(quotient>1) ans.add(new Edge(1, quotient));
	    return ans;
	}
	
	
	
	private static int INF = (int)1e8;
	private static long INFL = (long)1e17;
	private static long e97 = (long)1e9 + 7;
	
	
	private static int abs(int a){  return (a>=0) ? a: -a;  }
	private static long abs(long a){    return (a>=0) ? a: -a;  }
	private static double abs(double a){    return (a>=0) ? a: -a;  }
	
	private static int min(int a, int b){   return (a>b) ? b : a;   }
	private static long min(long a, long b){    return (a>b) ? b : a;   }
	private static double min(double a, double b){    return (a>b) ? b : a;   }
	
	private static int max(int a, int b){   return (a>b) ? a : b;   }
	private static long max(long a, long b){    return (a>b) ? a : b;   }
	private static double max(double a, double b){    return (a>b) ? a : b;   }
	
	private static int minN(int... ins){
		int min = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] < min) min = ins[i];  }
		return min;
	}
	private static int maxN(int... ins){
		int max = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] > max) max = ins[i];  }
		return max;
	}
	private static long minN(long... ins){
		long min = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] < min) min = ins[i];  }
		return min;
	}
	private static long maxN(long... ins){
		long max = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] > max) max = ins[i];  }
		return max;
	}
	
	private static int minExAd(int[] dt, int ad){
	    int min=INF;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static long minExAd(long[] dt, int ad){
	    long min=INFL;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static int minExVal(int[] dt, int ex_val){
	    int min=INF;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static long minExVal(long[] dt, long ex_val){
	    long min=INFL;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static int maxExAd(int[] dt, int ad){
	    int max=-INF;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] > max)) max = dt[i]; }
		return max;
	}
	private static long maxExAd(long[] dt, int ad){
	    long max=-INFL;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] > max)) max = dt[i]; }
		return max;
	}
	private static int maxExVal(int[] dt, int ex_val){
	    int max=-INF;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] > max)) max = dt[i]; }
		return max;
	}
	private static long maxExVal(long[] dt, long ex_val){
	    long max=-INFL;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] > max)) max = dt[i]; }
		return max;
	}

    private static long sumArray(long[] dt){
        long sum =0;
        for(int i=0; i<dt.length; i++){ sum += dt[i]; }
		return sum;
    }
	
	private static boolean same3(long a, long b, long c){
    	if(a!=b) return false;
    	if(b!=c) return false;
    	if(c!=a) return false;
    	return true;
	}
	private static boolean dif3(long a, long b, long c){
    	if(a==b) return false;
    	if(b==c) return false;
    	if(c==a) return false;
    	return true;
	}
	private static boolean triangle_inequality(int a, int b, int c){
	    if((a+b)<c) return false;
	    if((b+c)<a) return false;
	    if((c+a)<b) return false;
	    return true;
	}
	
	private static double hypod(double a, double b){
	    return Math.sqrt(a*a+b*b);
	}
	
	private static long factorial(int n) {
		long ans=1;
		for(long i=n; i>0; i--){ ans*=i; }
		return ans;
	}
	
	private static long facP(int n, long p) {
		long ans=1;
		for(long i=n; i>0; i--){
		    ans*=i;
		    ans %= p;
		}
		return ans;
	}
	
	private static long lcm(long m, long n){
	    long ans = m/gcd(m,n);
	    ans *= n;
	    return ans;
	}
	
	private static long gcd(long m, long n) {
		if(m < n) return gcd(n, m);
		if(n == 0) return m;
		return gcd(n, m % n);
	}
	
	private static boolean is_prime(long a){
	    if(a==1) return false;
	    for(int i=2; i<=Math.sqrt(a); i++){  if(a%i == 0) return false;  }
	    return true;
	}
	
    private static long modinv(long a, long p) {    //a|p, >1に注意
        long b = p, u = 1, v = 0;
        while (b>0) {
            long t = a / b;
            long pe = a%b;
            a=b;    b=pe;
            pe= u-t*v;
            u=v;    v=pe;
        }
        u %= p; 
        if (u < 0) u += p;
        return u;
    }
    
	private static int pow(int n, int k){
	    int ans=1;
	    for(int i=0; i<k; i++) ans *= n;
	    return ans;
	}
	
	private static int pow2(int in){            return in*in;   }
	private static long pow2(long in){          return in*in;   }
	private static double pow2(double in){      return in*in;   }
	
	private static int getDigit2(long num){
		long cf = 1;    int d=0;
		while(num >= cf){   d++;    cf = (1L<<d);  }
		
		return d; //numはd桁の数で、2^dより小さい
	}
	
	private static int getDigit10(long num){
		long cf = 1;    int d=0;
		while(num >= cf){   d++;    cf*=10;     }
		return d; //numはd桁の数で、10^dより小さい
	}
	
	private static boolean isINF(int in){
    	if(((long)in*20)>INF) return true;
    	else return false;
	}
	private static boolean isINFL(long in){
    	if((in*10000)>INFL) return true;
    	else return false;
	}
	
	private static long pow10E97(long ob, long soeji, long p){
	    if(ob==0) return 0;
	    if(soeji==0) return 1;
		if(soeji==2) return (ob*ob)%p;
		
		int d = getDigit2(soeji);
		long[] ob_pow_2pow = new long[d];
		
		ob_pow_2pow[0] = ob;
		for(int i=1; i<d; i++){ ob_pow_2pow[i] = (ob_pow_2pow[i-1]*ob_pow_2pow[i-1])%p;   }
		
		long ans=1;
		for(int i=d-1; i>=0; i--){
			if(soeji >= (long)(1<<i)){
				soeji -= (long)(1<<i);
				ans = (ans*ob_pow_2pow[i])%p;
			}
 		}
		return ans;
	}
	
	
	private static long flag(long pos){               return (1L<<pos);        }
	private static boolean isFlaged(int bit, int pos){
    	if((bit&(1<<pos)) > 0) return true;
    	else return false;
	}
	private static boolean isFlaged(long bit, int pos){
    	if((bit&(1L<<pos)) > 0) return true;
    	else return false;
	}
	private static int deflag(int bit, int pos){    return bit&~(1<<pos);   }
	private static int countFlaged(int bit){
	    int ans=0; 
	    for(int i=0; i<getDigit2(bit); i++){
	        if((bit&(1<<i)) > 0) ans++;
	    }
	    return ans;
	}
	
	private static void showflag(int bit){
    	for(int i=0; i<getDigit2(bit); i++){
        	if(isFlaged(bit,i)) System.out.print("O");
        	else System.out.print(".");
    	}
    	System.out.println();
	}
	
	public static int biSearch(int[] dt, int target){
		int left=0, right=dt.length-1;
		int mid=-1;
		while(left<=right){
			mid = (right+left)/2;
			if(dt[mid] == target) return mid;
			if(dt[mid] < target) left=mid+1;
			else right=mid-1;
		}
		return -1;
	}
	public static int biSearchMax(long[] dt, long target){
		int left=-1, right=dt.length;
		int mid=-1;
		
		while((right-left)>1){
			mid = left + (right-left)/2;
			if(dt[mid] <= target) left=mid;
			else right=mid;
		}
		return left;//target以下の最大のaddress
	}
	public static int biSearchMaxAL(ArrayList<Integer> dt, long target){
		int left=-1, right=dt.size();
		int mid=-1;
		
		while((right-left)>1){
			mid = left + (right-left)/2;
			if(dt.get(mid) <= target) left=mid;
			else right=mid;
		}
		return left;//target以下の最大のaddress
	}
	
	private static void fill_parent(int[] ob){
	    for(int i=0; i<ob.length; i++) ob[i]=i;
	}
    private static int get_root_uf(int[] parent, int index){
        if(parent[index] == index) return index;
        int root = get_root_uf(parent, parent[index]);
        parent[index] = root;
        return root;
    }
    private static boolean is_same_uf(int[] parent, int x, int y){
        if(get_root_uf(parent,x) == get_root_uf(parent,y)) return true;
        else return false;
    }
    private static void unite_uf(int[] parent, int receiver, int attacker){
        parent[get_root_uf(parent,attacker)] = get_root_uf(parent, receiver);
    }
	
    private static int[] Xdir4 = {1,0,0,-1};
    private static int[] Ydir4 = {0,1,-1,0};
	    
	private	static int[] Xdir8 = {1,1,1,0,0,-1,-1,-1};
	private	static int[] Ydir8 = {1,0,-1,1,-1,1,0,-1};
	
	private static boolean is_in_area(int y, int x, int h, int w){
	    if(y<0) return false;
	    if(x<0) return false;
	    if(y>=h) return false;
	    if(x>=w) return false;
	    return true;
	}
	
	
	static void show2(boolean[][] dt, int lit_x, int lit_y){
		PrintWriter out = new PrintWriter(System.out);
		for(int j=0; j<dt.length; j++){
		    for(int i=0; i<dt[j].length; i++){
				if((i==lit_y) && (j==lit_x)) out.print("X");
				else if(dt[j][i]) out.print("O");
				else out.print(".");
			}
			out.println();
		}
		out.flush();
	}
	static void show2(int[][] dt, String cmnt){
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<dt.length; i++){
			for(int j=0; j<dt[i].length; j++){
				out.print(dt[i][j]+",");
			}
			out.println("<-"+cmnt+":"+i);
		}
		out.flush();
	}
	static void show2(long[][] dt, String cmnt){
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<dt.length; i++){
			for(int j=0; j<dt[i].length; j++){
				out.print(dt[i][j]+",");
			}
			out.println("<-"+cmnt+":"+i);
		}
		out.flush();
	}
	static void disp_que(ArrayDeque<Long> dt){		//上手くいかなかった時用
		long a=0;
		while(dt.size()>0){
			a=dt.removeFirst();
			System.out.print(a);
		}
		System.out.println("\n");
	}
	static void disp_list(List dt){		//上手くいかなかった時用
	   	for(int i=0; i<dt.size(); i++){
			System.out.print(dt.get(i)+",");
		}
		System.out.println("\n");
	}
	
	
	private static void prtlnas(int[] as){
		PrintWriter out = new PrintWriter(System.out);
	    for(int i=0; i<as.length; i++){
	        out.println(as[i]);
	    }
	    out.flush();
	}
	private static void prtlnas(long[] as){
		PrintWriter out = new PrintWriter(System.out);
	    for(int i=0; i<as.length; i++){
	        out.println(as[i]);
	    }
	    out.flush();
	}
	private static void prtspas(int[] as){
		PrintWriter out = new PrintWriter(System.out);
		out.print(as[0]);
	    for(int i=1; i<as.length; i++){
	        out.print(" "+as[i]);
	    }
	    out.println();
	    out.flush();
	}
	private static void prtspas(long[] as){
		PrintWriter out = new PrintWriter(System.out);
		out.print(as[0]);
	    for(int i=1; i<as.length; i++){
	        out.print(" "+as[i]);
	    }
	    out.println();
	    out.flush();
	}
	private static void prtspas(List as){
		PrintWriter out = new PrintWriter(System.out);
		out.print(as.get(0));
	    for(int i=1; i<as.size(); i++){
	        out.print(" "+as.get(i));
	    }
	    out.println();
	    out.flush();
	}
	
	
    private static void fill(boolean[] ob, boolean res){    for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
    private static void fill(int[] ob, int res){            for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(long[] ob, long res){          for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(char[] ob, char res){          for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(double[] ob, double res){      for(int i=0; i<ob.length; i++){ ob[i] = res;    }}
	private static void fill(boolean[][] ob,boolean res){for(int i=0;i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(int[][] ob, int res){      for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(long[][] ob, long res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(char[][] ob, char res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(double[][] ob, double res){for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
	private static void fill(int[][][] ob,int res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
	
	static class UF_Pressed {
	    private HashMap<Integer,Integer> parent = new HashMap<>();
	    
        int get_root_uf(int index){
            if(parent.get(index) == index) return index;
            int root = get_root_uf(parent.get(index));
            parent.put(index,root);
            return root;
        }
        boolean is_same_uf(int x, int y){
            if(get_root_uf(x) == get_root_uf(y)) return true;
            else return false;
        }
        void unite_uf(int receiver, int attacker){
            parent.put(get_root_uf(attacker), get_root_uf(receiver));
        }
        
        void add(int e){
            if(!parent.containsKey(e)) parent.put(e,e);
        }
        
        void parent_is_me(int x){
            parent.put(get_root_uf(x),x);
            parent.put(x,x);
        }
        
        void disp(){
            for(int e: parent.values()) System.out.println(get_root_uf(e));
        }
        
        int size(){
            Set<Integer> set = new HashSet<>();
            for(int e: parent.values()){
                if(get_root_uf(e)>'9') set.add(get_root_uf(e));
            }
            return set.size();
        }
	}
    
    static class FastScanner {
    	private final InputStream in = System.in;
    	private final byte[] buffer = new byte[1024];
    	private int ptr = 0;
    	private int buflen = 0;
    	private boolean hasNextByte() {
    		if (ptr < buflen) {
    			return true;
    		}else{
    			ptr = 0;
    			try {
    				buflen = in.read(buffer);
    			} catch (IOException e) {
    				e.printStackTrace();
    			}
    			if (buflen <= 0) {
    				return false;
    			}
    		}
    		return true;
    	}
    	
    	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    	public String next() {
    		if (!hasNext()) throw new NoSuchElementException();
    		StringBuilder sb = new StringBuilder();
    		int b = readByte();
    		while(isPrintableChar(b)) {
    			sb.appendCodePoint(b);
    			b = readByte();
    		}
    		return sb.toString();
    	}
    	public long nexL() {
    		if (!hasNext()) throw new NoSuchElementException();
    		long n = 0;
    		boolean minus = false;
    		int b = readByte();
    		if (b == '-') {
    			minus = true;
    			b = readByte();
    		}
    		if (b < '0' || '9' < b) {
    			throw new NumberFormatException();
    		}
    		while(true){
    			if ('0' <= b && b <= '9') {
    				n *= 10;
    				n += b - '0';
    			}else if(b == -1 || !isPrintableChar(b) || b == ':'){
    				return minus ? -n : n;
    			}else{
    				throw new NumberFormatException();
    			}
    			b = readByte();
    		}
    	}
    	public int nexI() {
    		long nl = nexL();
    		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
    		return (int) nl;
    	}
    	public double nexD() { return Double.parseDouble(next());}
    	
    	public void ni(long[] array2){
    	   	for(int i=0; i<array2.length; i++){
    	   	    array2[i] = nexL();
    	   	}
    	   	return;
    	}
    	public void ni(int[] array2){
    	   	for(int i=0; i<array2.length; i++){
    	   	    array2[i] = nexI();
    	   	}
    	   	return;
    	}
    	public void ni(int[] as, int[] bs){
    	   	for(int i=0; i<as.length; i++){
    	   	    as[i] = nexI();
    	   	    bs[i] = nexI();
    	   	}
    	   	return;
    	}
    	public void ni(int[] as, int[] bs, int[] cs){
    	   	for(int i=0; i<as.length; i++){
    	   	    as[i] = nexI();
    	   	    bs[i] = nexI();
    	   	    cs[i] = nexI();
    	   	}
    	   	return;
    	}
    }
}