K-based Numbers. Version 2
Let’s consider K-based numbers, containing exactly N digits. We define a number to be valid if its K-based notation doesn’t contain two successive zeros. For example:
· 1010230 is a valid 7-digit number;
· 1000198 is not a valid number;
· 0001235 is not a 7-digit number, it is a 4-digit number.
Given two numbers N and K, you are to calculate an amount of valid K based numbers, containing N digits.
You may assume that 2 ≤ K ≤ 10; N ≥ 2; N + K ≤ 180.
The numbers N and K in decimal notation separated by the line break.
The result in decimal notation.