Score : $400$ points

问题陈述

给定两个正整数 $N$ 和 $M$。

找出满足以下两个条件的最小正整数 $X$，若不存在这样的整数，则输出 $-1$。

• $X$ 可以表示为两个在闭区间 $1$ 到 $N$ 内（包括两端点）的整数 $a$ 和 $b$ 的乘积。这里，$a$ 和 $b$ 可以是相同的。
• $X$ 至少为 $M$。

以上为通义千问 qwen-max 翻译，仅供参考。

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.

Sample Input 1

5 7

Sample Output 1

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 $8$.

Sample Input 2

2 5

Sample Output 2

-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 $-1$.

Sample Input 3

100000 10000000000

Sample Output 3

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.

update @ 2024/3/10 12:18:10