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   Problem Statement  

 Problem Statement for SimilarSequencesAnother

Problem Statement

    

Two sequences A and B are called similar if they have the same length and have the following property: we can obtain two identical sequences by deleting at most two elements of A and at most two elements of B. (The elements deleted from A don't have to have the same indices as the elements deleted from B. The order of the remaining elements in each sequence has to be preserved.)

You are given ints N and bound. Consider all the sequences with length N such that each element is an integer between 1 and bound, inclusive. Compute the number of ordered pairs of such sequences that are similar. Return this count modulo 1,000,000,009.

 

Definition

    
Class:SimilarSequencesAnother
Method:getCount
Parameters:int, int
Returns:int
Method signature:int getCount(int N, int bound)
(be sure your method is public)
    
 

Constraints

-N will be between 1 and 100, inclusive.
-bound will be between 1 and 1,000,000,000, inclusive.
 

Examples

0)
    
2
10
Returns: 10000
Any two 2-element sequences are similar. There are (10^2)^2 = 10,000 pairs of such sequences.
1)
    
3
3
Returns: 687
In this case, two sequences are similar if they have at least one element in common. In other words, the two sequences are similar if there is a value that occurs in each of them. Let's count the pairs of sequences that are not similar. There are two possibilities:
  • Each sequence contains the same value three times. For example, one sequence could be {1,1,1} and the other {3,3,3}. There are 6 such pairs.
  • One sequence contains the same value three times, and the other contains the other two values, each of them at least once. For example, one sequence could be {2,3,2} and the other {1,1,1}. There are 2 * 3 * (2^3 - 2) = 36 such pairs.
Thus, the total number of pairs of similar sequences is 3^6 - 6 - 36 = 687.
2)
    
8
1
Returns: 1
3)
    
100
123456789
Returns: 439681851
4)
    
1
1000000000
Returns: 81

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This problem was used for:
       Single Round Match 619 Round 1 - Division I, Level Three