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 (1 ≤ b, w ≤ 1000) - number of black and white areas.

Output

The first line should contain the picture sizes r and c (1 ≤ r, c ≤ 100 000) - 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.