Cut a Rectangle


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A given rectangle is made from m × n squares. If m and n are not both odd, then it is possible to cut a path through the rectangle along the square edges such that the rectangle splits into two connected pieces with the same shape (after rotating one of the pieces by 180°). All such paths for 2 × 2 and 4 × 3 rectangles are shown below.

cut rectangles

Challenge

You will be given pairs of integers m and n. Print out the number of different ways to cut an m × n rectangle.

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