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1013. K-based Numbers. Version 3

Time limit: 0.5 second
Memory limit: 64 MB
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.

Input

The numbers N, K and M in decimal notation separated by the line break.

Output

The result in decimal notation.

Sample

inputoutput
2
10
100
90