1009. K-based Numbers
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 two numbers
N and
K, you are to calculate an amount of valid
K based numbers, containing
Ndigits.
You may assume that 2 ≤
K ≤ 10;
N ≥ 2;
N +
K ≤ 18.
Input
The numbers
N and
K in decimal notation separated by the line break.
Output
The result in decimal notation.
Sample
Problem Source: USU Championship 1997