A. k-rounding

Codeforces

IDCF861A

Time1000ms

Memory256MB

Difficulty—

mathnumber theory

English · Original

Chinese · Translation

Formal · Original

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_. For 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. Write a program that will perform the _k_\-rounding of _n_. ## Input The only line contains two integers _n_ and _k_ (1 ≤ _n_ ≤ 109, 0 ≤ _k_ ≤ 8). ## Output Print the _k_\-rounding of _n_. [samples]

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。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。编写一个程序，计算 $n$ 的 $k$-rounding。输入仅一行，包含两个整数 $n$ 和 $k$（$1 ≤ n ≤ 10^9$，$0 ≤ k ≤ 8$）。请输出 $n$ 的 $k$-rounding。 ## Input 输入仅一行，包含两个整数 $n$ 和 $k$（$1 ≤ n ≤ 10^9$，$0 ≤ k ≤ 8$）。 ## Output 请输出 $n$ 的 $k$-rounding。 [samples]

**Definitions** Let $ n \in \mathbb{Z}^+ $, $ k \in \mathbb{Z} $ with $ 0 \leq k \leq 8 $. The $ k $-rounding of $ n $ is the smallest positive integer $ x $ such that: - $ n \mid x $, - $ x \equiv 0 \pmod{10^k} $. **Objective** Find $ x = \min \{ y \in \mathbb{Z}^+ \mid n \mid y \text{ and } 10^k \mid y \} $. **Solution Formulation** $$ x = \frac{\mathrm{lcm}(n, 10^k)}{\gcd(n, 10^k)} \cdot \gcd(n, 10^k) = \mathrm{lcm}(n, 10^k) $$ Thus, $$ x = \mathrm{lcm}(n, 10^k) $$

Samples

Input #1

375 4

Output #1

Input #2

10000 1

Output #2

Input #3

38101 0

Output #3

Input #4

123456789 8

Output #4

12345678900000000

API Response (JSON)

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    "name": "A. k-rounding",
    "description": {
      "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_. For example, 4\\-rounding o",
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      "time_limit": 1000,
      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "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 o...",
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    {
      "statement_type": "Markdown",
      "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...",
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      "statement_type": "Markdown",
      "content": "**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 \\...",
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