Long Domino#4258

Long Domino

5 seconds
256 megabytes
Easy

Determine the number of ways to completely cover an m \times n rectangle using dominoes that are each 3 \times 1 in size. Each domino must fit entirely within the rectangle, and no two dominoes can overlap. Dominoes may be placed either horizontally or vertically.

Input

You will be given two integers, and , where 1 \leq m \leq 9 and 1 \leq n \leq 30.

Output

Print the number of distinct ways to tile the m \times n rectangle using the dominoes.

Examples

Example 1

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