{"raw_statement":[{"iden":"statement","content":"For a given positive integer _n_ denote its _k_\\-rounding as the minimum positive integer _x_, such that _x_ ends with _k_ or more zeros in base 10 and is divisible by _n_.\n\nFor example, 4\\-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.\n\nWrite a program that will perform the _k_\\-rounding of _n_."},{"iden":"input","content":"The only line contains two integers _n_ and _k_ (1 ≤ _n_ ≤ 109, 0 ≤ _k_ ≤ 8)."},{"iden":"output","content":"Print the _k_\\-rounding of _n_."},{"iden":"examples","content":"Input\n\n375 4\n\nOutput\n\n30000\n\nInput\n\n10000 1\n\nOutput\n\n10000\n\nInput\n\n38101 0\n\nOutput\n\n38101\n\nInput\n\n123456789 8\n\nOutput\n\n12345678900000000"}],"translated_statement":[{"iden":"statement","content":"对于给定的正整数 $n$，定义其 $k$-rounding 为最小的正整数 $x$，使得 $x$ 在十进制下以 $k$ 个或更多零结尾，且能被 $n$ 整除。\n\n例如，$375$ 的 $4$-rounding 是 $375·80 = 30000$。$30000$ 是满足以 $4$ 个或更多零结尾且能被 $375$ 整除的最小整数。\n\n编写一个程序，计算 $n$ 的 $k$-rounding。\n\n输入仅一行，包含两个整数 $n$ 和 $k$（$1 ≤ n ≤ 10^9$，$0 ≤ k ≤ 8$）。\n\n请输出 $n$ 的 $k$-rounding。"},{"iden":"input","content":"输入仅一行，包含两个整数 $n$ 和 $k$（$1 ≤ n ≤ 10^9$，$0 ≤ k ≤ 8$）。"},{"iden":"output","content":"请输出 $n$ 的 $k$-rounding。"},{"iden":"examples","content":"输入\n375 4\n输出\n30000\n\n输入\n10000 1\n输出\n10000\n\n输入\n38101 0\n输出\n38101\n\n输入\n123456789 8\n输出\n12345678900000000"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z}^+ $, $ k \\in \\mathbb{Z} $ with $ 0 \\leq k \\leq 8 $.  \nThe $ k $-rounding of $ n $ is the smallest positive integer $ x $ such that:  \n- $ n \\mid x $,  \n- $ x \\equiv 0 \\pmod{10^k} $.\n\n**Objective**  \nFind $ x = \\min \\{ y \\in \\mathbb{Z}^+ \\mid n \\mid y \\text{ and } 10^k \\mid y \\} $.\n\n**Solution Formulation**  \n$$ x = \\frac{\\mathrm{lcm}(n, 10^k)}{\\gcd(n, 10^k)} \\cdot \\gcd(n, 10^k) = \\mathrm{lcm}(n, 10^k) $$  \nThus,  \n$$ x = \\mathrm{lcm}(n, 10^k) $$","simple_statement":null,"has_page_source":false}