SP28413 ADAFENCE - Ada and Fence

Ada the Ladybug owns a circular land. She wants to enclose it with fence. Anyway since nobody sells round planks, she has decided to fence it to shape of regular **k-gon**. Problem is, that there is only limited number or places (on circle) where pilars can be built. Ada has asked you, to find out the number of different regular **k-gon** shaped fences which can be built on her land (two **k-gon**'s are considered different if they share NO common pillar).

The first line will contain **T**, the number of test-cases. Then **T** test-cases follow, each beginning with two integers **3 , **3 , the number of places where pillar can be built and number of edges of regular **k-gon****** Afterward a line with **N** integers **1 follow, meaning the length of arc between two consecutive points where pillar can be built. The sum of all lengths will be divisible by **K**.** Sum of **N** over all test-cases won't exceed **2\*10 $ ^{6} $**

For each test-case print the number of different regular **k-gon** shaped fences which can be built.