You are given a 2D plane. Initially, two points (P_1) and (P_2) are located at ((0,0)) and ((1,0)), respectively, with a line segment connecting them. You can draw triangles using the following operation: Choose two points (A) and (B) that are directly connected by a line segment (i.e., (A) and (B) must be the endpoints of an existing segment). Choose two real numbers (x) and (y) such that (-2\cdot 10^4\le x, y\le 2\cdot 10^4). Draw a new point (C) at coordinates ((x,y)). Then, draw line segments (AC) and (BC), forming triangle (\triangle ABC). The length (l) of every side of the new triangle (\triangle ABC) must satisfy (0.5\le l\le 1). Note that each operation draws one new point and two new line segments. Your task is to draw a point at coordinates ((p, q)) using at most (m = \left\lceil 2\sqrt{p^2 + q^2}\right\rceil) operations, where (\lceil x\rceil) is the smallest integer greater than or equal to (x). It is guaranteed that (p) and (q) are positive integers. Due to potential rounding errors: The constructed vertex only needs to be within (10^{-4}) of ((p,q)). For triangle side lengths, an absolute error of (10^{-8}) is allowed (i.e., (0.5 - 10^{-8} \le l \le 1 + 10^{-8})). Note that the target point may be created before the last operation (see the second test case). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 1000)). The description of the test cases follows. The first line of each test case contains three integers (p), (q), and (m) ((1\le p, q\le 10^4), (m = \left\lceil 2\sqrt{p^2 + q^2}\right\rceil)) — the (x) and (y) coordinates of the target, and the maximum number of operations you are allowed to perform, respectively. It is guaranteed that the sum of (m) over all test cases does not exceed (10^5). For each test case, output