_{This problem is a programming version of Problem 237 from projecteuler.net}

Let be the number of tours over an playing board such that:

• The tour starts in the top left corner;
• The tour consists of moves that are up, down, left, or right one square;
• The tour visits each square exactly once;
• The tour ends in the bottom left corner.

The following diagram shows one tour over a board:

Define = . It can be shown that and .

Given integers and , what is ?
Since the answer can be quite large, express your solution modulo .