Painting Storages（ZOJ)

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<N, M<=100,000).

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

 #include <stdio.h>
 #include <string.h>
 const int N = 1e5 + ;
 const int mod = 1e9 + ;
 int dp[N],pow[N]= {};

 int main()
 {
     int n,m;
     for(int i=; i<N; i++) pow[i] = pow[i-] *  % mod;
     while(~scanf("%d%d",&n,&m))
     {
         memset(dp,,sizeof(int)*m);
         dp[m] = ;
         for(int i=m+; i<=n; i++) dp[i] = ((dp[i-]* % mod + pow[i-m-]-dp[i-m-]) % mod + mod) % mod;
         printf("%d\n",dp[n]);
     }
     return ;
 }

数论（排列组合）