ural 1012K-based Numbers. Version 2 1013. K-based Numbers. Version 3

1013. K-based Numbers. Version 3

Time Limit: 2.0 second
Memory Limit: 64 MB

Let’s consider K-based numbers, containing exactly N digits. We define a number to be valid if itsK-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 Ndigits.

You may assume that 2 ≤ K ≤ 10; N ≥ 2; N + K ≤ 1800.

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

import java.io.*;
import java.util.*;
import java.math.*;

public class aa{
public static void main(String args[]){
Scanner cin = new Scanner(new BufferedInputStream(System.in));
int n = cin.nextInt(),k = cin.nextInt();
BigInteger  dp[] = new BigInteger[2000];
dp[1] = BigInteger.valueOf(k-1);
dp[2] = BigInteger.valueOf(k*(k-1));
for(int i = 3; i <= n ; i ++ ){
dp[i] = BigInteger.valueOf(0).add(dp[i-1]).add(dp[i-2]);
dp[i] = dp[i].multiply(BigInteger.valueOf(k-1));
}
System.out.println(dp
);
}
}