{"raw_statement":[{"iden":"statement","content":"Ehsan loves geometry! Especially he likes to rotate points!\n\nGiven a point in the plane, Ehsan likes to rotate it by _k_ degrees (counter-clockwise), around the origin. What is the result of this rotation?"},{"iden":"input","content":"A single integer _k_ (0 ≤ _k_ < 360) is given in the first line. Two integer numbers _x_ and _y_ are given in the second line ( - 1390 ≤ _x_, _y_ ≤ 1390)."},{"iden":"output","content":"Write two numbers. The result of the rotation. Your answer must have a relative error less than 10 - 1."},{"iden":"examples","content":"Input\n\n90\n1 1\n\nOutput\n\n\\-1.00000000 1.00000000\n\nInput\n\n180\n1 1390\n\nOutput\n\n\\-1.00000000 -1390.00000000"}],"translated_statement":[{"iden":"statement","content":"Ehsan 热爱几何！尤其是他喜欢旋转点！\n\n给定平面上的一个点，Ehsan 喜欢将其绕 #cf_span(class=[tex-font-style-underline], body=[origin]) 逆时针旋转 #cf_span[k] 度。旋转后的结果是什么？\n\n第一行给出一个整数 #cf_span[k]（#cf_span[0 ≤ k < 360]）。第二行给出两个整数 #cf_span[x] 和 #cf_span[y]（#cf_span[ - 1390 ≤ x, y ≤ 1390]）。\n\n请输出两个数，即旋转后的结果。你的答案的相对误差必须小于 #cf_span[10 - 1]。\n\n"},{"iden":"input","content":"第一行给出一个整数 #cf_span[k]（#cf_span[0 ≤ k < 360]）。第二行给出两个整数 #cf_span[x] 和 #cf_span[y]（#cf_span[ - 1390 ≤ x, y ≤ 1390]）。"},{"iden":"output","content":"请输出两个数，即旋转后的结果。你的答案的相对误差必须小于 #cf_span[10 - 1]。"},{"iden":"examples","content":"输入901 1输出-1.00000000 1.00000000输入1801 1390输出-1.00000000 -1390.00000000"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ k \\in \\mathbb{Z} $ with $ 0 \\leq k < 360 $ be the rotation angle in degrees.  \nLet $ (x, y) \\in \\mathbb{R}^2 $ be the coordinates of the point to be rotated about the origin.\n\n**Constraints**  \n$ -1390 \\leq x, y \\leq 1390 $\n\n**Objective**  \nCompute the rotated point $ (x', y') $ obtained by rotating $ (x, y) $ counter-clockwise by $ k $ degrees about the origin:  \n$$\n\\begin{aligned}\nx' &= x \\cos \\theta - y \\sin \\theta \\\\\ny' &= x \\sin \\theta + y \\cos \\theta\n\\end{aligned}\n$$  \nwhere $ \\theta = \\frac{\\pi k}{180} $ radians.  \n\nOutput $ (x', y') $ with relative error less than $ 10^{-1} $.","simple_statement":null,"has_page_source":false}