102963: [Atcoder]ABC296 D - M<=ab

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.

问题描述

给你两个正整数$N$和$M$。

• $X$可以表示为两个在$1$到$N$（含）之间的整数$a$和$b$的乘积。这里，$a$和$b$可以相同。
• $X$至少为$M$。

约束

• $1\leq N\leq 10^{12}$
• $1\leq M\leq 10^{12}$
• $N$和$M$是整数。

输入

输入将从标准输入按以下格式给出：

$N$ $M$

输出

输出满足两个条件的最小正整数$X$，如果没有这样的整数，则输出$-1$。

样例输入1

5 7

样例输出1

8

首先，$7$不能表示为两个在$1$到$5$之间的整数的乘积。

其次，$8$可以表示为两个在$1$到$5$之间的整数的乘积，如$8=2\times 4$。

因此，你应该输出$8$。

样例输入2

2 5

样例输出2

-1

由于$1\times 1=1$，$1\times 2=2$，$2\times 1=2$，$2\times 2=4$，只有$1$，$2$和$4$可以表示为两个在$1$到$2$之间的整数的乘积，所以没有大于等于$5$的数可以表示为两个这样的整数的乘积。

因此，你应该输出$-1$。

样例输入3

100000 10000000000

样例输出3

10000000000

对于$a=b=100000$ $(=10^5)$，$a$和$b$的乘积为$10000000000$ $(=10^{10})$，这就是答案。

注意答案可能不适用32位整数类型。