### K-based Numbers. Version 2

Time Limit: 1000 ms
Memory Limit: 65536 KiB

#### Problem Description

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.

#### Input

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

#### Output

The result in decimal notation.

#### Sample Input

2 10

#### Sample Output

90