ural 1012

1012. K-based Numbers. Version 2

Time limit: 0.5 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 ≤ 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

轉移方程和ural 1009 一樣。不過數據加大了。。這樣會導致溢出。 java大法好！

<pre name="code" class="java">import java.math.BigInteger;
import java.util.Scanner;

public class Main {
			static Scanner s = new Scanner(System.in);
			static BigInteger dp[][] = new BigInteger[1900][3];
			public static void main(String[] args) {
				int n = s.nextInt();
				BigInteger k  = s.nextBigInteger();
				dp[1][0] = k.subtract(new BigInteger("1"));
				dp[1][1] = new BigInteger("0");
				for(int i=2; i<=n; i++){
					dp[i][0] = dp[i-1][1].add(dp[i-1][0]).multiply(dp[1][0]);
					dp[i][1] = dp[i-1][0];
				}
				BigInteger res = dp[n][0].add(dp[n][1]);
				System.out.println(res);
			}
}