K-based Numbers

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:
(1)1010230 is a valid 7-digit number;
(2)1000198 is not a valid number;
(3)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 ≤ 18.

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

Hint


Source