URAL 1513. Lemon Tale(简单的递推)

写几组数据就会发现规律了啊。

。但是我是竖着看的。。

。还找了半天啊、、、

只是要用高精度来写，水题啊。就当熟悉一下java了啊。

num[i] = 2*num[i-1]-num[i-2-k]。

1513. Lemon Tale

Time limit: 1.0 second

Memory limit: 64 MB

Background

For each programmer a point comes when the last contest is lost, and it is time to retire. Even Three Programmers themselves could not escape the common lot. But the Programmers also wanted to keep
a good memory about themselves. For this noble purpose they created problems and organized extremely popular programming contests from time to time. Of course, this work was not well paid, but for true programmers a glory was more important than money.

However it is only the first half of a job to think out a brilliant problem. The second one is to create a politically correct statement for it.

Problem

The matter is the statement of some problem for the upcoming contest was written by the Third Programmer, who knew nothing about political correctness. He just wrote a story about citrus plants growing.
As a result a word "lemon" was mentioned N times in the statement.

Besides, the problem is to be looked through by famous censor Alexander K. right before the contest. And it is a known fact, that lemons remind him of oranges he hates furiously. It worries the First
and the Second Programmers greatly - they know exactly, that if a word "lemon" occurs more than Ktimes successively, the problem will be immediately disqualified from the contest.

That is why the First and the Second Programmers connived secretly to login to the server at the eve of the contest and replace some "lemons" with much more politically correct "bananas" so that the
problem could not be disqualified. How many ways are there to do it?

Input

The only line contains the integer numbers N (1 ≤ N ≤ 10000) and K (0 ≤ K ≤ N).

Output

You should output the desired number of ways.

Sample

input	output
5 2	24

Hint

Let us denote a word "lemon" by a letter "L" and a word "banana" by a letter "B". So in the sample the initial sequence of words "LLLLL" might be transformed into the following politically correct sequences:
"LLBLL", "LLBLB", "LLBBL", "LLBBB", "LBLLB", "LBLBL", "LBLBB", "LBBLL", "LBBLB", "LBBBL", "LBBBB", "BLLBL", "BLLBB", "BLBLL", "BLBLB", "BLBBL", "BLBBB", "BBLLB", "BBLBL", "BBLBB", "BBBLL", "BBBLB", "BBBBL" and "BBBBB".

import java.math.BigInteger;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner cin = new Scanner(System.in);
		int n, k;
		BigInteger num[] = new BigInteger [100005];
		while(cin.hasNext())
		{
			n = cin.nextInt();
			k = cin.nextInt();
			BigInteger ans;
			BigInteger p = BigInteger.valueOf(2);
			ans = p.pow(n);
			if(k == 0)
			{
				System.out.println(1);
				continue;
			}
			if(n == k)
			{
				System.out.println(ans);
				continue;
			}
			num[0] = BigInteger.valueOf(1);
			for(int i = 1; i <= k+1; i++)
			{
				num[i] = p.pow(i-1);
			}
			for(int i = k+2; i <= n; i++)
			{
				num[i] = num[i-1].multiply(BigInteger.valueOf(2));
				num[i] = num[i].subtract(num[i-2-k]);
			}
			ans = BigInteger.valueOf(0);
			for(int i = n; i >= (n-k); i--)
			{
				ans = ans.add(num[i]);
			}
			System.out.println(ans);
		}
	}
}