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Competitions

1/8 ICPC Azerbaijan Qualification Preparation

Black and White

The jury has a great artistic idea - to create a rectangular panel out of a huge pile of black and white squares of the same size. The panel should have exactly b 4-connected areas made of black tiles, and w 4-connected areas made of white tiles.

Remember, a 4-connected area of some color is a maximal set of the panel tiles such that:

  • any two tiles of the area share the same color;
  • for any two tiles of the area there is a tile sequence connecting them, such that any two consecutive tiles of the sequence share a common side.

In addition to the artistic idea, the jury has already developed a program that produces design of the panel. But since this problem is about art, any new solution is extremely important for the jury.

Input

The only line contains two integers b and w (1b, w1000) - number of black and white areas.

Output

The first line should contain the picture sizes r and c (1r, c100 000) - the number of rows and columns. This line should be followed by r lines of c symbols each. Each symbol should be either '@' (for black tile) or '.' (for white one). There should be no more than 100 000 tiles in the panel.

Time limit 1 second
Memory limit 128 MiB
Input example #1
2 3
Output example #1
4 6
.@.@@@
@@@@@@
......
.@....
Source 2015 ACM NEERC, Northern Subregion, October 24, Problem B