JOIN

 Problem Statement

Problem Statement for CharacterBoard

### Problem Statement

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:
• 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.
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.

### Definition

 Class: CharacterBoard Method: countGenerators Parameters: String[], int, int, int Returns: int Method signature: int countGenerators(String[] fragment, int W, int i0, int j0) (be sure your method is public)

### Constraints

-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.

### Examples

0)

 ```{"dea", "abc"} ``` `7` `1` `1`
`Returns: 1`
 Manao has a matrix with 1000000000 rows and 7 columns. We know that it looks as follows: ```??????? ?dea??? ?abc??? ??????? ... ``` The only string of length at most 7 which could generate such matrix is "abcde".
1)

 ```{"xyxxy"} ``` `6` `1` `0`
`Returns: 28`
 The given information is: ```?????? xyxxy? ?????? ... ``` The corresponding generator could be "xyx", "yxyxx", or a string of form "xyxxy?", where '?' stands for any lowercase letter.
2)

 ```{"gogogo", "jijiji", "rarara"} ``` `6` `0` `0`
`Returns: 0`
 No generator could create this matrix using the given algorithm.
3)

 ```{"abababacac", "aaacacacbb", "ccabababab"} ``` `8827` `104` `6022`
`Returns: 829146844`

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This problem was used for:
Single Round Match 576 Round 1 - Division I, Level Three