Triangular Pizza
Mamma Triangolo baked a triangular pizza. She wants to cut the pizza into pieces. She first chooses a point in the interior (not boundary) of the triangle pizza, and then performs cuts, which all start from and extend straight to the boundary of the pizza so that the pieces are all triangles and all have the same area.
Let be the number of different ways for Mamma Triangolo to cut the pizza, subject to the constraints.
For example, .
Also , and .
Let . You are given and .
Find . Give your answer modulo .
三角形披萨
特莱格伦夫人打算把一块三角形的披萨分成片。她先在三角形披萨的内部(而非边缘)选择一个点,然后从点出发切刀至披萨边缘,将披萨分成个面积相同的小三角形。
记为满足特莱格伦夫人上述要求的披萨切法。
例如,。
此外,,。
记。已知,。
求,并将你的答案对取余。
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