ural 1009. Kbased Numbers

1009. K-based Numbers

Time Limit: 1.0 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 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	output
2 10	90

#include <iostream>
#include <algorithm>

#define MAX 20
using namespace std;

int dp[MAX]={0};

int main(){
    int n,k;
    cin >> n >> k;
    dp[1] = k-1;
    dp[2] =k*(k-1);
    for(int i = 3; i <= n; i ++ ){
        dp[i] = (k-1)*dp[i-1]+(k-1)*dp[i-2];
    }
    cout<< dp[n]<<endl;
    return 0;
}