{"problem":{"name":"H. Robocon Club","description":{"content":"Ahmed thought that robotics is fun so he quit ACM and joined Robocon club ! Unfortunately his first task at the Robocon Club did not go as well as he expected. He was supposed to build a robot that mo","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":65536},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10106H"},"statements":[{"statement_type":"Markdown","content":"Ahmed thought that robotics is fun so he quit ACM and joined Robocon club ! Unfortunately his first task at the Robocon Club did not go as well as he expected. He was supposed to build a robot that moves in a straight line. \n\nThe robot he had built consists of a line segment of length L with a wheel of radius R on each of it's endpoints. He placed the robot on the x axis, such that the center of the robot was the point (0, 0) , facing the positive y axis (the left and right wheels are located on  and  respectively). \n\nThe two wheels started moving at the same time, however, instead of moving at the same speed, the left wheel rotated at VL revolutions per second(RPS), while the right wheel rotated at VR RPS. both wheels stopped moving after S seconds. Can you help Ahmed locate the center of his robot? \n\nThe first line of the input consists of a single integer T , the number of test cases. T lines follow , each describing a test case consisting of five integers L , R , VL , VR , S . indicating the length of the robot , the radius of each wheel , the speed of the left wheel in (RPS), the speed of the right wheel in (RPS) and the duration that the robot had moved , respectively . where (1 ≤ L ≤ 100 ,1 ≤ R ≤ 100 ,0 ≤ VL ≤ 100 ,0 ≤ VR ≤ 100 , 1 ≤ S ≤ 100 ) . \n\nfor each test case print two real numbers on a line separated by a space denotes the coordinates of the center of the robot rounded to three decimal places . \n\n## Input\n\nThe first line of the input consists of a single integer T , the number of test cases. T lines follow , each describing a test case consisting of five integers L , R , VL , VR , S . indicating the length of the robot , the radius of each wheel , the speed of the left wheel in (RPS), the speed of the right wheel in (RPS) and the duration that the robot had moved , respectively . where (1 ≤ L ≤ 100 ,1 ≤ R ≤ 100 ,0 ≤ VL ≤ 100 ,0 ≤ VR ≤ 100 , 1 ≤ S ≤ 100 ) . \n\n## Output\n\nfor each test case print two real numbers on a line separated by a space denotes the coordinates of the center of the robot rounded to three decimal places . \n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ N, M \\in \\mathbb{Z}^+ $ denote the number of songs for Taylor Swift and Katy Perry, respectively.  \nLet $ A = (a_1, \\dots, a_N) \\in (\\mathbb{Z}^+)^N $ be the sequence of song qualities for Taylor.  \nLet $ B = (b_1, \\dots, b_M) \\in (\\mathbb{Z}^+)^M $ be the sequence of song qualities for Katy.  \n\nThe **Glauber mean** of a non-empty multiset $ S = \\{x_1, \\dots, x_k\\} \\subseteq \\mathbb{Z}^+ $ is defined as:  \n$$\n\\text{GlauberMean}(S) = \\frac{\\prod_{x \\in S} x}{|S|}\n$$\n\n**Constraints**  \n1. $ 1 \\le N, M \\le 50 $  \n2. $ 1 \\le a_i, b_j \\le 100 $ for all $ i, j $  \n\n**Objective**  \nDetermine whether there exist non-empty subsets $ A' \\subseteq A $, $ B' \\subseteq B $ such that:  \n$$\n\\frac{\\prod_{x \\in A'} x}{|A'|} = \\frac{\\prod_{y \\in B'} y}{|B'|}\n$$  \nIf such subsets exist:  \n- Output \"Y\", followed by $ |A'| $, $ |B'| $, then the elements of $ A' $ and $ B' $.  \n- Otherwise, output \"N\".","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10106H","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}