Score : $400$ points

Problem Statement

You are given positive integers $N$ and $M$. Find the smallest positive integer $X$ that satisfies both of the conditions below, or print $-1$ if there is no such integer.

• $X$ can be represented as the product of two integers $a$ and $b$ between $1$ and $N$, inclusive. Here, $a$ and $b$ may be the same.
• $X$ is at least $M$.

Constraints

• $1\leq N\leq 10^{12}$
• $1\leq M\leq 10^{12}$
• $N$ and $M$ are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$

Output

Print the smallest positive integer $X$ that satisfies both of the conditions, or $-1$ if there is no such integer.

5 7

8

First, $7$ cannot be represented as the product of two integers between $1$ and $5$. Second, $8$ can be represented as the product of two integers between $1$ and $5$, such as $8=2\times 4$.

Thus, you should print $8$.

2 5

-1

Since $1\times 1=1$, $1\times 2=2$, $2\times 1=2$, and $2\times 2=4$, only $1$, $2$, and $4$ can be represented as the product of two integers between $1$ and $2$, so no number greater than or equal to $5$ can be represented as the product of two such integers. Thus, you should print $-1$.

100000 10000000000

10000000000

For $a=b=100000$ $(=10^5)$, the product of $a$ and $b$ is $10000000000$ $(=10^{10})$, which is the answer. Note that the answer may not fit into a $32$-bit integer type.