Description

To make the graduation party better, the teacher wants to select $k$ students with the highest compatibility to participate in the rehearsal. But how to choose? The teacher lists all student numbers $1, 2, \ldots, n$ and believes that the compatibility level of $k$ students is their greatest common divisor (this is not superstition~). This is difficult for him, so please help!

PS: The greatest common divisor of a single number is the number itself.

Input Format

Two space-separated positive integers $n$ and $k$.

Output Format

A single integer: the maximum compatibility value.

4 2

2

Hint

For $20\%$ of the testdata, $k \le 2$, $n \le 10^3$.

For another $30\%$ of the testdata, $k \le 10$, $n \le 100$.

For $100\%$ of the testdata, $k \le 10^9$, $n \le 10^9$, $n \ge k \ge 1$ (a "Shenben" school, many students).

Translated by ChatGPT 5