CF425E.Sereja and Sets

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 (109 + 7).

假设集合 $S$ 由 $m$ 个互不相同的区间 $[l_1,\,r_1]$, $[l_2,\,r_2]$, …, $[l_m,\,r_m]$ 组成（其中 $1 \le l_i \le r_i \le n$；$l_i,\,r_i$ 均为整数）。

定义 $f(S)$ 为：从集合 $S$ 中最多能选出多少个互不相交的区间。我们称两个区间 $[l_1,\,r_1]$ 与 $[l_2,\,r_2]$ 相交，当且仅当存在某个整数 $x$ 同时满足不等式 $l_1 \le x \le r_1$ 和 $l_2 \le x \le r_2$。

Sereja 想知道：满足 $f(S) = k$ 的集合 $S$ 共有多少个？答案对 $1000000007$（即 $10^9 + 7$）取模。

The first line contains integers n, k (1 ≤ n ≤ 500; 0 ≤ k ≤ 500).

第一行包含整数 $n$、$k$（$1 ≤ n ≤ 500$；$0 ≤ k ≤ 500$）。

In a single line, print the answer to the problem modulo 1000000007 (109 + 7).

在一行中输出该问题的答案对 1000000007（$10^9 + 7$）取模的结果。