Timus 1009

K-based Numbers

Time Limit: 1.0 second

Memory Limit: 16 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 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

output

90

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int res[30];
int main()
{
    int i,k,n;
    while(scanf("%d %d",&n,&k)!=EOF)
    {
        if(n==1)
        {
            printf("%d\n",k);
            continue;
        }
        res[1]=k-1;
        res[2]=(k-1)*k;
        for(i=3;i<=n;i++)
            res[i]=(k-1)*(res[i-1]+res[i-2]);
        printf("%d\n",res[n]);
    }
    return 0;
}