Kinky Word Searches

문제

You're probably familiar with regular word searches, where you're presented with a grid of letters and a word to find.  The word can be in a straight line horizontally, vertically, or diagonally (and perhaps backwards in any of those directions).  For example, here is a grid of letters:

Figure 1: A word search grid

The word "JAVA" can be found going from the bottom right corner diagonally upwards.

In a kinky word search the path that spells out the word can have one or more "kinks" -- places where the path changes direction.  For example, in the given grid you can spell the word "PYTHON" with $33$ kinks (one each at the T, H and  O):

Figure 2: A kinky spelling of "PYTHON"

Adding kinks allows letters to be reused -- the word "CPLUSPLUS" can be found in the upper right corner of the grid (with $55$ kinks).  However you cannot stay on a letter twice in a row, so you cannot spell the word "HASKELL" in this grid (though you can find at least $1111$ more common programming languages). Your task is to see if the spelling of a word with a certain number of kinks is possible or not.

입력

Input begins with a line containing two positive integers $rr$ and $cc$ ($r,c\le 10)r,\; c\; \backslash leq\; 10)$, the number of rows and columns in the grid.  After this are $rr$ rows of $cc$ uppercase characters.  Letters are separated by a space. After the grid are two lines: The first line is an integer $kk$, the number of kinks.  The second line contains an uppercase word to look for, with maximum length $100100$.

출력

Output either the word YES if it is possible to spell the given word with exactly $kk$ kinks on the grid provided, or NO if it is not.

5 5
L M E L C
C A K U P
D O V S Y
R N L A T
P G O H J
0
JAVA

YES

5 5
L M E L C
C A K U P
D O V S Y
R N L A T
P G O H J
3
PYTHON

YES

5 5
L M E L C
C A K U P
D O V S Y
R N L A T
P G O H J
4
PYTHON

NO