KIT Finding

문제

"Find the Fox" is a recent book that contains $200200$ pages of word search puzzles comprising only the letters 'F', 'O' and 'X'. The special feature of the book is that there is only a single occurrence of the word "FOX" throughout all of its pages.

Recall that in a word search the goal is to find hidden words (only one hidden word in this case) in a grid of letters. The words can occur horizontally or vertically or diagonally, as well as forwards or backwards, allowing for a total of $88$ different reading directions.

For this year's NWERC, we want to create a baby version of "Find the Fox". Your goal in this problem, therefore, is to create a word search grid with given dimensions and containing each of the letters 'K', 'I' and 'T' a given number of times. Similar to the original book, this grid should contain exactly one occurrence of the word "KIT".

Figure K.1: Illustration of Sample Output 1. Flip page for the solution.

입력

The input consists of:

• One line with five integers $hh$, $ww$, $kk$, $ii$, and $tt$ ($3\le h,w\le 1003\; \backslash le\; h,w\; \backslash le\; 100$, $k,i,t\ge 1k,i,t\; \backslash ge\; 1$, $k+i+t=h\cdot wk+i+t\; =\; h\backslash cdot\; w$), where $hh$ and $ww$ are the height and width the word search grid should have, and $kk$, $ii$, and $tt$ specify the required number of occurrences of 'K', 'I' and 'T', respectively.

출력

Output a word search grid according to the given rules. It can be shown that such a word search grid always exists.

If there are multiple valid solutions, you may output any one of them.

힌트