M<=ab

AtCoder

IDabc296_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $M$ [samples]

Samples

Input #1

5 7

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 $8$.

Input #2

2 5

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 $-1$.

Input #3

100000 10000000000

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.

API Response (JSON)

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      "content": "You are given positive integers $N$ and $M$.  \nFind the smallest positive integer $X$ that satisfies both of the conditions below, or print $-1$ if there is no such integer.\n\n*   $X$ can be represente...",
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