ZOJ 3725 Painting Storages（很好的dp题）

There is a straight highway with N storages alongside it labeled by 1,2,3,...,N. Bob asks you to paint all storages with two colors: red and blue. Each storage will be painted with exactly one color.

Bob has a requirement: there are at least M continuous storages (e.g. "2,3,4" are 3 continuous storages) to be painted with red. How many ways can you paint all storages under Bob's requirement?

Input

There are multiple test cases.

Each test case consists a single line with two integers: N and M (0

Process to the end of input.

Output

One line for each case. Output the number of ways module 1000000007.

Sample Input

4 3 

Sample Output

3

题目链接：Click here~~

题意：

n个格子排成一条直线，可以选择涂成红色或蓝色，问至少有m 个连续格子为红色的方案数。

解释一下这个：

dp[i]=(dp[i-1]*2%mod+mod_pow(2,i-m-1,mod)-dp[i-m-1]%mod+mod)%mod;

dp[i-1]*2指前i-1个已经符合条件，第i个可红可蓝，所以*2

mod_pow(2,i-m-1,mod)-dp[i-m-1]%mod指的是前i-1个还不符合条件，但是加上第i位（红色）就符合了条件的情况数。第i-m位必须为蓝（隔断），前i-m-1位可红可蓝，所以mod_pow(2,i-m-1,mod)，但是要排除前i-m-1位符合条件的情况，所以-dp[i-m-1]。第i-m位的后面都是红色格子。

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