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. One line for each case. Output the number of ways module 1000000007. Output
Sample Input
4 3
Sample Output
3
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