Div Times Mod

题意翻译

## 题目描述 给定n,k(1≤n≤$10^6$,2≤k≤$10^3$) 已知i，ans $\in$ Z，S.T. i | n（1≤i)&&ans $\equiv$ i(mod k)&&ans / k == n / i 求ans的最小值 ## 输入输出格式 ### 输入格式： 一行，分别为n,k ### 输出格式： 一行，ans ## 输入输出样例 样例搬运过来就行了

题目描述

Vasya likes to solve equations. Today he wants to solve $ (x~\mathrm{div}~k) \cdot (x \bmod k) = n $ , where $ \mathrm{div} $ and $ \mathrm{mod} $ stand for integer division and modulo operations (refer to the Notes below for exact definition). In this equation, $ k $ and $ n $ are positive integer parameters, and $ x $ is a positive integer unknown. If there are several solutions, Vasya wants to find the smallest possible $ x $ . Can you help him?

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 1 \leq n \leq 10^6 $ , $ 2 \leq k \leq 1000 $ ).

输出格式

Print a single integer $ x $ — the smallest positive integer solution to $ (x~\mathrm{div}~k) \cdot (x \bmod k) = n $ . It is guaranteed that this equation has at least one positive integer solution.

输入输出样例

输入样例 #1

6 3

输出样例 #1

11

输入样例 #2

1 2

输出样例 #2

3

输入样例 #3

4 6

输出样例 #3

10

说明

The result of integer division $ a~\mathrm{div}~b $ is equal to the largest integer $ c $ such that $ b \cdot c \leq a $ . $ a $ modulo $ b $ (shortened $ a \bmod b $ ) is the only integer $ c $ such that $ 0 \leq c < b $ , and $ a - c $ is divisible by $ b $ . In the first sample, $ 11~\mathrm{div}~3 = 3 $ and $ 11 \bmod 3 = 2 $ . Since $ 3 \cdot 2 = 6 $ , then $ x = 11 $ is a solution to $ (x~\mathrm{div}~3) \cdot (x \bmod 3) = 6 $ . One can see that $ 19 $ is the only other positive integer solution, hence $ 11 $ is the smallest one.