Block stacking

Yeongseon can use as many blocks of size $1 \times 1 \times 1$, $1 \times 1 \times 2$, and $1 \times 1 \times 3$ as she wants. She also has one block of size $1 \times 1 \times w$, which is called the base block.

Yeongseon builds a structure from one base block and the other blocks. Every block must be connected to the base block, and no block can be placed at a non-integer position. A long block ($1 \times 1 \times 2$ or $1 \times 1 \times 3$) must have both of its ends resting on other blocks. For a $1 \times 1 \times 3$ block, the cell under its middle part may be empty.

The picture on the left is a valid structure. The picture on the right cannot be built.

The height of a structure is the number of layers stacked on top of the base block. The structure with no block at all has height $0$, and it counts as one structure.

Given the length $w$ of the base block and the height limit $h$, write a program that counts the structures of height at most $h$ that can be built from one base block and an unlimited number of the other blocks.

The picture below shows all 84 structures for $w = 3$ and $h = 2$.

The first line contains $w$ and $h$, separated by a space. ($1 \le w, h \le 10$)

Print the number of structures modulo $1000000007$ on the first line.