| ||Manao has a matrix X with 1,000,000,000 rows and W columns. He likes to fill it with characters; he even has developed an algorithm for this task. First, he chooses a string S consisting of at most W lowercase letters. The string S is called the generator. Then, he applies the algorithm described by the following pseudocode:
cur := 0
for i := 0 to 999999999
for j := 0 to W - 1
X[i][j] := S.charAt(cur)
cur := (cur + 1) mod length(S)
Manao has recently found a matrix X in his notepad.
He wonders whether it was generated using the above algorithm.
You are given:
In other words, for all valid i, j we have fragment[i][j] = X[i + i0][j + j0].
Count how many different generators Manao could have used to create a matrix X that contains the fragment you were given.
Return this number modulo 1,000,000,009.
- a String fragment that contains a rectangular submatrix of X,
- the int W: the width of X,
- and two ints i0 and j0: the coordinates of the upper left corner of your submatrix within X.
|Parameters:||String, int, int, int|
|Method signature:||int countGenerators(String fragment, int W, int i0, int j0)|
|(be sure your method is public)|
|-||fragment will contain N elements, where N is between 1 and 10, inclusive.|
|-||Each element of fragment will be M characters long, where M is between 1 and 10, inclusive.|
|-||Each element of fragment will consist of lowercase letters ('a'-'z') only.|
|-||W will be between M and 1,000,000,000, inclusive.|
|-||i0 will be between 0 and 1,000,000,000 - N, inclusive.|
|-||j0 will be between 0 and W - M, inclusive.|
|Manao has a matrix with 1000000000 rows and 7 columns. We know that it looks as follows:
The only string of length at most 7 which could generate such matrix is "abcde".
|The given information is:
The corresponding generator could be "xyx", "yxyxx", or a string of form "xyxxy?", where '?' stands for any lowercase letter.
|No generator could create this matrix using the given algorithm.
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