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 three numbers N, K and M, you are to calculate an amount of valid K based numbers, containing N digits modulo M.
You may assume that 2 ≤ N, K, M ≤ 1018.
The numbers N, K and M in decimal notation separated by the line break.
The result in decimal notation.