Problem:
Score : 500 points

Problem Statement

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.

Notes

Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.

A set of squares painted white, S, forms a connected component when the following conditions are met:

Any two squares in S are connected.

No pair of a square painted white that is not included in S and a square included in S is connected.

A connected component of squares painted black is defined similarly.

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 #.

Sample Input 1

2 3

Sample Output 1

3 3
##.
..#
#.#

This output corresponds to the grid below:

Sample Input 2

7 8

Sample Output 2

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

Sample Input 3

1 1

Sample Output 3

4 2
..
#.
##
##

Sample Input 4

3 14

Sample Output 4

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

Solution in Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

var a,b,t:longint;
    num,bool,y,where:longint;
    i,j:longint;
    map:Array[0..105,0..105]of longint;
    c1,c2:char;
begin
  read(a,b);
  c1:='.';
  c2:='#';
  if a>b then
  begin
    t:=a;a:=b;b:=t;
    c1:='#';
    c2:='.';
  end;
  b:=b-a+1;
  if a=1 then dec(b);
  num:=1;
  bool:=0;
  while a>0 do
  begin
    inc(num);
    bool:=1-bool;
    for i:=1 to num-1 do
    begin
      map[i,num-i]:=bool;
      if bool=1 then dec(a);
      if a=0 then break;
    end;
  end;
  for j:=1 to num-1 do
  begin
    map[num,j]:=0;
    map[num+1,j]:=1;
  end;
  inc(num);
  y:=num;
  for i:=1 to num do
  map[i,num-1]:=1;
  if b<>0 then
  begin
    while num<100 do
    begin
      inc(num);
      if num mod 2=1 then
      begin
        for j:=1 to y-1 do
        map[num,j]:=1;
      end else
      begin
        for j:=1 to y-1 do
        begin
          if (j mod 2=0) then map[num,j]:=1 else dec(b);
          if b=0 then
          begin
            where:=j;
            break;
          end;
        end;
      end;
      if b=0 then
      begin
        for j:=where+1 to y-1 do
        map[num,j]:=1;
        break;
      end;
    end;
  end;
  dec(y);
  while b>0 do
  begin
    inc(y);
    for i:=1 to num do
    begin
      if i mod 2=0 then map[i,y]:=1 else dec(b);
      if b=0 then
      begin
        where:=i;
        break;
      end;
    end;
    inc(y);
    for i:=1 to num do
    map[i,y]:=1;
    if b=0 then
    begin
      for i:=where+1 to num do
      map[i,y-1]:=1;
    end;
  end;
  writeln(num,' ',y);
  for i:=1 to num do
  begin
    for j:=1 to y do
    write(map[i,j],' ');
    writeln;
  end;
end.