Consonant words' scale X47203

Definition 1: A pair of words written in capital letters ($p_1, p_2$) is said to form a consonant scale if the number of occurrences of consonants in $p_2$ is greater than the number of occurrences of consonants in $p_1$.

For example, the pair (MADUIXOT, PRESSEC) form a consonant scale, since MADUIXOT has 4 consonants and PRESSEC has 5. So does the pair (POMA, PLATAN). However, neither (SINDRIA, PRUNA) nor (PERA, KIWI) do form a consonant scale.

Definition 2: A consonant words’ scale of length $k$ is a sequence of $k$ words (written in capital letters), where every pair of consecutive words of the sequence form a consonant scale.

For example: POMA, MADUIXA, PLATAN, PRESSEC, ALBERCOCS is a consonant words’ scale of words with length 5.

Definition 3: Given a matrix with $n$ rows and $m$ columns, we say that a sequence of $k$ positions of the matrix is scaled if it follows the following form $\{(i,j), (i+1, j+1),..., (i+k-1, j+k-1)\}$, for $i, j, k$ holding that $0\leq i$, $i+k-1 < n$, $0\leq j$, $j+k-1<m$.

For example, given a matrix of size $6\times 10$, the sequence $\{(0,2),(1,3),(2,4),(3,5),(4,6)\}$ is a scaled sequence of positions of length 5, that starts at position $(0,2)$

To do:

Do a program that, given a word matrix and a natural $k$, traverses the matrix in a row-wise way and computes the first position $(i,j)$ starting a consonant words’ scale of length $k$ in a scaled sequence of positions starting at $(i,j)$.

Your program must represent the word matrix by means of the following type:

struct Word {
     string contents;           // the word
     int consonants;            // number of occurrences of consonants 
};
 
typedef vector< vector<Word> > WordsMat;

Input

The input is composed by a single case. The case consists of the number of rows $n\geq 1$, the number of columns $m\geq 1$ of the matrix, and a natural number $k$ determining the length of the sequence to be found. Following, we find $n$ lines with $m$ strings each. Each string is formed only by capital letters.

Output

You must write in a single line: the row number and the column number of the matrix, together with the word in it, where the first (according to a row-wise traversal) consonant words’ scale of length $k$ starts when considering a scaled sequence of positions. You must write -1 -1 when the matrix does not have any.

Follow the format as specified on the examples. Follow a good programming style. You may consider (but it is up to you) to include comments within your code.