{"raw_statement":[{"iden":"statement","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_."},{"iden":"input","content":"The first line contains two integers _n_ and _k_ (2 ≤ _n_ ≤ 100000, 1 ≤ _k_ ≤ 20)."},{"iden":"output","content":"If 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."},{"iden":"examples","content":"Input\n\n100000 2\n\nOutput\n\n2 50000 \n\nInput\n\n100000 20\n\nOutput\n\n\\-1\n\nInput\n\n1024 5\n\nOutput\n\n2 64 2 2 2"}],"translated_statement":[{"iden":"statement","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"},{"iden":"input","content":"第一行包含两个整数 $n$ 和 $k$（$2 ≤ n ≤ 100000$，$1 ≤ k ≤ 20$）。"},{"iden":"output","content":"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。"},{"iden":"examples","content":"输入\n100000 2\n输出\n2 50000 \n\n输入\n100000 20\n输出\n-1\n\n输入\n1024 5\n输出\n2 64 2 2 2 "}],"sample_group":[],"show_order":[],"formal_statement":"**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 $-1$.","simple_statement":null,"has_page_source":false}