K-based Numbers

K-based Numbers

Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status Practice URAL 1009

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 ≤ 18.

Input

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

Output

The result in decimal notation.

Sample Input

input	output
2 10	90

例如：n = 3;

　　dp[3] = 

　　　　　　1, 2, 3 + (1, 2, 3 + 0, 1, 2, 3); k*dp[2];

　　　　　　+

　　　　　　10, 20, 30 + 1, 2, 3; k*dp[1];

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int dp[15];
int main(){
    int n, k;
    scanf("%d%d", &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] + dp[i-2]);
    }
    printf("%d\n",dp[n]);
    return 0;
}