Migrated from Lutece 1268 Open the lightings

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Description

There are $n$ light(s) in a row.These lights are numbered $1$ to $n$ from left to right.One of the lights are switched on.I wants to switch all the lights on. At each step I can switch a light on(this light should be switched off at that moment)if there's at least one "very close" light which is already switched on. More exactly: when No.$i$ light(this light is switched on now),No.$j$ light can be switched on(this light is switched off now) if and only if $|i-j|<=2$. I knows the initial state of lights and I wonder how many different ways there exist to switch all the lights on.

Please find the required number of ways modulo $1000000007 (10^9+7)$.

Input

The first line of the input contains two integers $n$ and $m$ where $n$ is the number of lights in the sequence and No.$m$ light are initially switched on,$(1<=n<=1000,1<=m<=n)$.

Output

In the only line of the output print the number of different possible ways to switch on all the lights modulo $1000000007 (10^9+7)$.

Samples

3 1

2

Resources

第七届ACM趣味程序设计竞赛第四场（正式赛）