127 - ZOJ Monthly, June 2013 - J
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?
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.
One line for each case. Output the number of ways module 1000000007.
Author: ZHAO, Kui