ExtendedHappyNumbers | Topcoder Archive

Problem Statement

Given a positive integer N, raise each of its digits to the K-th power and sum those values to get S_K(N). For example, S₂(65) = 6² + 5² = 61. Now, consider a sequence N, S_K(N), S_K(S_K(N)) and so on. The happiness of N with respect to K is the smallest number in this sequence.

You will be given three ints A, B and K. Calculate the happiness of each integer between A and B, inclusive, with respect to K and return their sum.

Definition

Class:: ExtendedHappyNumbers
Method:: calcTheSum
Parameters:: int, int, int
Returns:: long
Method signature:: long calcTheSum(int A, int B, int K)
(be sure your method is public)

Constraints

A will be between 1 and 1,000,000, inclusive.
B will be between A and 1,000,000, inclusive.
K will be between 1 and 6, inclusive.

Examples

```
13
```
```
13
```
```
2
```
```
Returns: 1
```
The sequence for 13 is 13, 10, 1, 1...
```
1
```
```
5
```
```
2
```
```
Returns: 14
```
The sequences for numbers 1 to 5 are: 1: 1, 1, 1... 2: 2, 4, 16, 37, 58, 89, 145, 42, 20, 4... 3: 3, 9, 81, 65, 61, 37, 58, 89, 145, 42, 20, 4, 16, 37... 4: 4, 16, 37, 58, 89, 145, 42, 20, 4... 5: 5, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, 89...
```
10
```
```
99
```
```
1
```
```
Returns: 450
```
```
535
```
```
538
```
```
3
```
```
Returns: 820
```
```
100000
```
```
400000
```
```
6
```
```
Returns: 5169721292
```

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