ural 1012Kbased Numbers. Version 2 1013. Kbased 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[n]);
	}
}