Sereja and Sets

### 题目描述 对于一个有 $m$ 条线段的集合 $S$ 来说，定义函数 $f(S)$ 为你最多可以从这个集合中选择多少线段使得他们都不相交。端点重合也算相交。线段的右端点都小于等于 $n$。 对于给定的 $n,k$，求出有多少个满足条件的 $S$ 满足 $f(S)=k$。 ### 输入格式 输入仅一行，$n,k$。$(1\le n\le 500,\ \ 0\le k\le 500)$。 ### 输出格式 输出一行一个正整数，表示答案。对 $10^9+7$ 取模。

Let's assume that set $ S $ consists of $ m $ distinct intervals $ [l_{1},r_{1}] $ , $ [l_{2},r_{2}] $ , $ ... $ , $ [l_{m},r_{m}] $ ( $ 1<=l_{i}<=r_{i}<=n $ ; $ l_{i},r_{i} $ are integers). Let's assume that $ f(S) $ is the maximum number of intervals that you can choose from the set $ S $ , such that every two of them do not intersect. We assume that two intervals, $ [l_{1},r_{1}] $ and $ [l_{2},r_{2}] $ , intersect if there is an integer $ x $ , which meets two inequalities: $ l_{1}<=x<=r_{1} $ and $ l_{2}<=x<=r_{2} $ . Sereja wonders, how many sets $ S $ are there, such that $ f(S)=k $ ? Count this number modulo $ 1000000007 $ $ (10^{9}+7) $ .

The first line contains integers $ n $ , $ k $ $ (1<=n<=500; 0<=k<=500) $ .

In a single line, print the answer to the problem modulo $ 1000000007 $ $ (10^{9}+7) $ .

3 1

23

3 2

32

2 0

1

2 2

2