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.