Contest Duration: - (local time) (100 minutes) Back to Home
F - Solitaire /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

すぬけくんは N 枚のカードとデック(両端キュー)で遊ぶことにしました。 カードには 1,2,3...,N の数が書かれており、デックははじめ空です。

すぬけくんは 1,2,3,...,N が書かれたカードをこの順に、それぞれデックの先頭あるいは末尾に挿入します。 その後、すぬけくんはデックの先頭あるいは末尾からカードを取り出して食べる、という操作を N 回行います。

### 制約

• 1 ≦ K ≦ N ≦ 2{,}000

### 入力

N K


### 入力例 1

2 1


### 出力例 1

1


• 1,2 のどちらもカードの山の一番下に挿入する
• カードの山の一番上からカードを取り出して食べることを 2 回行う

### 入力例 2

17 2


### 出力例 2

262144


### 入力例 3

2000 1000


### 出力例 3

674286644


Score : 1200 points

### Problem Statement

Snuke has decided to play with N cards and a deque (that is, a double-ended queue). Each card shows an integer from 1 through N, and the deque is initially empty.

Snuke will insert the cards at the beginning or the end of the deque one at a time, in order from 1 to N. Then, he will perform the following action N times: take out the card from the beginning or the end of the deque and eat it.

Afterwards, we will construct an integer sequence by arranging the integers written on the eaten cards, in the order they are eaten. Among the sequences that can be obtained in this way, find the number of the sequences such that the K-th element is 1. Print the answer modulo 10^{9} + 7.

### Constraints

• 1 ≦ K ≦ N ≦ 2{,}000

### Input

The input is given from Standard Input in the following format:

N K


### Output

Print the answer modulo 10^{9} + 7.

### Sample Input 1

2 1


### Sample Output 1

1


There is one sequence satisfying the condition: 1,2. One possible way to obtain this sequence is the following:

• Insert both cards, 1 and 2, at the end of the deque.
• Eat the card at the beginning of the deque twice.

### Sample Input 2

17 2


### Sample Output 2

262144


### Sample Input 3

2000 1000


### Sample Output 3

674286644