A12183. Div Times Mod

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?

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

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.

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.