{"problem":{"name":"A. k-Factorization","description":{"content":"Given a positive integer _n_, find _k_ integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to _n_.","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF797A"},"statements":[{"statement_type":"Markdown","content":"Given a positive integer _n_, find _k_ integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to _n_.\n\n## Input\n\nThe first line contains two integers _n_ and _k_ (2 ≤ _n_ ≤ 100000, 1 ≤ _k_ ≤ 20).\n\n## Output\n\nIf it's impossible to find the representation of _n_ as a product of _k_ numbers, print _\\-1_.\n\nOtherwise, print _k_ integers in any order. Their product must be equal to _n_. If there are multiple answers, print any of them.\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"给定一个正整数 $n$，找出 $k$ 个整数（不必互不相同），使得这些整数均严格大于 $1$，且它们的乘积等于 $n$。\n\n第一行包含两个整数 $n$ 和 $k$（$2 ≤ n ≤ 100000$，$1 ≤ k ≤ 20$）。\n\n如果无法将 $n$ 表示为 $k$ 个数的乘积，请输出 _-1_。\n\n否则，请输出 $k$ 个整数（顺序任意）。它们的乘积必须等于 $n$。如果有多个答案，输出任意一个即可。\n\n## Input\n\n第一行包含两个整数 $n$ 和 $k$（$2 ≤ n ≤ 100000$，$1 ≤ k ≤ 20$）。\n\n## Output\n\n如果无法将 $n$ 表示为 $k$ 个数的乘积，请输出 _-1_。否则，输出 $k$ 个整数（顺序任意）。它们的乘积必须等于 $n$。如果有多个答案，输出任意一个即可。\n\n[samples]","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $, $ k \\in \\mathbb{Z} $ be given integers with $ 2 \\leq n \\leq 100000 $, $ 1 \\leq k \\leq 20 $.  \n\n**Objective**  \nFind $ k $ integers $ a_1, a_2, \\dots, a_k \\in \\mathbb{Z} $ such that:  \n- $ a_i > 1 $ for all $ i \\in \\{1, \\dots, k\\} $,  \n- $ \\prod_{i=1}^k a_i = n $.  \n\nIf no such tuple exists, output $-1$.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF797A","tags":["implementation","math","number theory"],"sample_group":[["100000 2","2 50000"],["100000 20","\\-1"],["1024 5","2 64 2 2 2"]],"created_at":"2026-03-03 11:00:39"}}