{"raw_statement":[{"iden":"statement","content":"A pair (p, q) of integer numbers is called Rasta - lover if and only if 1 ≤ p, q < n and there is a positive integer like x such that:\n\npx ≡ q (modn)\n\nSubtasks 1 - 3: \n\nGiven n, calculate the number of Rasta - lover pairs modulo 109 + 7.\n\nSubtasks 4 - 6:\n\nA positive integer p is called n - Rastaly if and only if p < n and there is a positive integer like x such that px ≡ 1 (modn) and p and n are coprimes.\n\nFor a positive integer n, f(n) is the smallest positive integer a such that for each n - Rastaly number like p, pa ≡ 1 (modn) (this number always exists).\n\nIf M is equal to  for a given A, then you have to calculate M modulo 109 + 7.\n\nSubtasks:\n\nEach subtask consists of one testcase.\n\nInput consists of one number. For subtasks 1-3, it's n and for subtasks 4-6 it's A.\n\nPrint the answer modulo 109 + 7 in one line.\n\n"},{"iden":"input","content":"Each subtask consists of one testcase.Input consists of one number. For subtasks 1-3, it's n and for subtasks 4-6 it's A."},{"iden":"output","content":"Print the answer modulo 109 + 7 in one line."},{"iden":"examples","content":""}],"translated_statement":[{"iden":"statement","content":"一对整数 #cf_span[(p, q)] 被称为 #cf_span[Rasta - lover]，当且仅当 #cf_span[1 ≤ p, q < n] 且存在一个正整数 #cf_span[x] 使得：\n\n#cf_span[px ≡ q] #cf_span[(modn)]\n\n子任务 #cf_span[1 - 3]：\n\n给定 #cf_span[n]，计算 #cf_span[Rasta - lover] 对的数量，对 #cf_span[109 + 7] 取模。\n\n子任务 #cf_span[4 - 6]：\n\n一个正整数 #cf_span[p] 被称为 #cf_span[n - Rastaly]，当且仅当 #cf_span[p < n] 且存在一个正整数 #cf_span[x] 使得 #cf_span[px ≡ 1] #cf_span[(modn)]，且 #cf_span[p] 与 #cf_span[n] 互质。\n\n对于正整数 #cf_span[n]，#cf_span[f(n)] 是最小的正整数 #cf_span[a]，使得对每个 #cf_span[n - Rastaly] 数 #cf_span[p]，都有 #cf_span[pa ≡ 1] #cf_span[(modn)]（这样的数总是存在）。\n\n如果给定 #cf_span[A] 时 #cf_span[M] 等于 ，则你需要计算 #cf_span[M] 对 #cf_span[109 + 7] 取模的结果。\n\n子任务：\n\n每个子任务包含一个测试用例。\n\n输入包含一个数。对于子任务 1-3，该数为 #cf_span[n]；对于子任务 4-6，该数为 #cf_span[A]。\n\n请在一行中输出答案对 #cf_span[109 + 7] 取模的结果。"},{"iden":"input","content":"每个子任务包含一个测试用例。输入包含一个数。对于子任务 1-3，该数为 #cf_span[n]；对于子任务 4-6，该数为 #cf_span[A]。"},{"iden":"output","content":"请在一行中输出答案对 #cf_span[109 + 7] 取模的结果。"},{"iden":"examples","content":""}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions:**\n\n- Let $ n \\in \\mathbb{Z}^+ $.\n- Let $ \\mathbb{Z}_n^* = \\{ p \\in \\mathbb{Z} : 1 \\leq p < n, \\gcd(p, n) = 1 \\} $ be the multiplicative group modulo $ n $.\n- Let $ \\lambda(n) $ denote the Carmichael function: the smallest positive integer $ a $ such that $ p^a \\equiv 1 \\pmod{n} $ for all $ p \\in \\mathbb{Z}_n^* $.\n\n---\n\n**Subtasks 1–3:**\n\nCount the number of pairs $ (p, q) \\in \\mathbb{Z}^2 $ such that:\n- $ 1 \\leq p, q < n $,\n- $ \\exists x \\in \\mathbb{Z}^+ $ such that $ p^x \\equiv q \\pmod{n} $.\n\nLet $ S(n) = \\left| \\left\\{ (p, q) \\in [1, n-1]^2 : \\exists x \\geq 1 \\text{ s.t. } p^x \\equiv q \\pmod{n} \\right\\} \\right| $.\n\nCompute $ S(n) \\mod (10^9 + 7) $.\n\n---\n\n**Subtasks 4–6:**\n\nGiven $ A \\in \\mathbb{Z}^+ $, compute $ f(n) = \\lambda(n) $, where $ n $ is the unique positive integer such that $ \\lambda(n) = A $.  \nIf no such $ n $ exists, the problem is undefined — but the input guarantees existence.\n\nCompute $ A \\mod (10^9 + 7) $.\n\n> **Note:** The problem states:  \n> *“If $ M $ is equal to for a given $ A $, then you have to calculate $ M $ modulo $ 10^9 + 7 $.”*  \n> This is malformed, but context implies $ M = \\lambda(n) = A $, so we are to output $ A \\mod (10^9 + 7) $.\n\n---\n\n**Final Formal Output:**\n\nFor input $ n $ (subtasks 1–3):  \n$$\n\\boxed{S(n) = \\left| \\left\\{ (p, q) \\in [1, n-1]^2 : \\exists x \\in \\mathbb{Z}^+,\\ p^x \\equiv q \\pmod{n} \\right\\} \\right| \\mod (10^9 + 7)}\n$$\n\nFor input $ A $ (subtasks 4–6):  \n$$\n\\boxed{A \\mod (10^9 + 7)}\n$$","simple_statement":null,"has_page_source":false}