{"problem":{"name":"C. Vectors","description":{"content":"At a geometry lesson Gerald was given a task: to get vector _B_ out of vector _A_. Besides, the teacher permitted him to perform the following operations with vector _А_: *   Turn the vector by 90 de","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF101C"},"statements":[{"statement_type":"Markdown","content":"At a geometry lesson Gerald was given a task: to get vector _B_ out of vector _A_. Besides, the teacher permitted him to perform the following operations with vector _А_:\n\n*   Turn the vector by 90 degrees clockwise.\n*   Add to the vector a certain vector _C_.\n\nOperations could be performed in any order any number of times.\n\nCan Gerald cope with the task?\n\n## Input\n\nThe first line contains integers _x_1 и _y_1 — the coordinates of the vector _A_ ( - 108 ≤ _x_1, _y_1 ≤ 108). The second and the third line contain in the similar manner vectors _B_ and _C_ (their coordinates are integers; their absolute value does not exceed 108).\n\n## Output\n\nPrint \"_YES_\" (without the quotes) if it is possible to get vector _B_ using the given operations. Otherwise print \"_NO_\" (without the quotes).\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"在一次几何课上，Gerald 被布置了一个任务：用向量 #cf_span[A] 得到向量 #cf_span[B]。此外，老师允许他对向量 #cf_span[A] 执行以下操作：\n\n这些操作可以以任意顺序执行任意多次。\n\nGerald 能否完成这个任务？\n\n第一行包含整数 #cf_span[x1] 和 #cf_span[y1] —— 向量 #cf_span[A] 的坐标（#cf_span[ - 108 ≤ x1, y1 ≤ 108]）。第二行和第三行以类似方式给出向量 #cf_span[B] 和 #cf_span[C]（它们的坐标为整数，绝对值不超过 #cf_span[108]）。\n\n如果可以通过给定操作得到向量 #cf_span[B]，请输出 \"_YES_\"（不含引号）；否则输出 \"_NO_\"（不含引号）。\n\n## Input\n\n第一行包含整数 #cf_span[x1] 和 #cf_span[y1] —— 向量 #cf_span[A] 的坐标（#cf_span[ - 108 ≤ x1, y1 ≤ 108]）。第二行和第三行以类似方式给出向量 #cf_span[B] 和 #cf_span[C]（它们的坐标为整数，绝对值不超过 #cf_span[108]）。\n\n## Output\n\n如果可以通过给定操作得到向量 #cf_span[B]，请输出 \"_YES_\"（不含引号）；否则输出 \"_NO_\"（不含引号）。\n\n[samples]","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ \\mathbf{A} = (x_1, y_1) $, $ \\mathbf{B} = (x_2, y_2) $, $ \\mathbf{C} = (x_3, y_3) $ be vectors in $ \\mathbb{Z}^2 $.\n\n**Constraints**  \nAll coordinates are integers: $ x_1, y_1, x_2, y_2, x_3, y_3 \\in \\mathbb{Z} $, and $ |x_i|, |y_i| \\leq 10^8 $ for $ i \\in \\{1,2,3\\} $.\n\n**Objective**  \nDetermine whether there exist integers $ m, n \\in \\mathbb{Z} $ such that:  \n$$\n\\mathbf{B} = \\mathbf{A} + m \\mathbf{C} + n (-\\mathbf{C})\n$$  \nor equivalently,  \n$$\n\\mathbf{B} - \\mathbf{A} = k \\mathbf{C} \\quad \\text{for some } k \\in \\mathbb{Z}.\n$$","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF101C","tags":["implementation","math"],"sample_group":[["0 0\n1 1\n0 1","YES"],["0 0\n1 1\n1 1","YES"],["0 0\n1 1\n2 2","NO"]],"created_at":"2026-03-03 11:00:39"}}