FIICode 2024 Open | Tree Count

The history of all hitherto existing society is the history of the struggle for better LOL ranks.

— Hungry Santa, 1848

We start with a binary tree consisting of only one node, namely its root. At each step, we can choose a leaf of the current tree and create two new children in that node, namely the left one and the right one. Find the total number of trees of height $h$ that can be obtained after applying $n$ such operations. The result shall be printed modulo $10^9 + 7$.

The height of a tree is defined as the length (that is, number of edges) of the longest path starting from its root and ending in one of its leaves.

Two binary trees, $T_1$ and $T_2$, each having more than one node, are considered equal if the left subtree of $T_1$ equals the left subtree of $T_2$ and the right subtree of $T_1$ equals the right subtree of $T_2$. Two binary trees, each having exactly one node, are always considered equal.

Input

The first line contains the numbers $n$ ($0 \le n \le 500$) and $h$ ($0 \le h \le 500$).

Output

The first line contains the required number modulo $10^9 + 7$.

Example 1

stdin

5 3

stdout

6

Example 2

stdin

314 100

stdout

569329628