Calling Extraterrestrial Intelligence Again

On the afternoon of Saturday, November 16, 1974, a message from humans to extraterrestrial intelligence was sent through the Arecibo radio telescope in Puerto Rico. The message consisted of 1679 bits and was meant to be read as a rectangular picture of 23 × 73 pixels. Since both 23 and 73 are prime numbers, 23 × 73 is the only possible size of the picture in which each edge is longer than 1 pixel. Of course, there was no guarantee that the receivers would try to read the message as a rectangular picture. Even if they did, they might place the pixels into the rectangle incorrectly. The senders of the Arecibo message were optimistic.

We are planning a similar project. Your task in the project is to find the most suitable width and height of the decoded rectangular picture. "Most suitable" is defined as follows. An integer $m$ greater than 4 is given. A positive fraction $a/b$ less than or equal to 1 is also given. The area of the picture must not be greater than $m$. Both the width and the height of the picture must be prime numbers. The ratio of the width to the height must be neither less than $a/b$ nor greater than 1. You have to maximize the area of the picture under these constraints.

In other words, you receive an integer $m$ and a fraction $a/b$ with $m > 4$ and $0 < a/b \le 1$. Find the pair of prime numbers $p$, $q$ such that $pq \le m$ and $a/b \le p/q \le 1$, and the product $pq$ is the maximum among all such pairs. Report $p$ and $q$ as the "most suitable" width and height of the picture.

The input is a sequence of at most 2000 triplets of positive integers. Each line contains one triplet, with a single space between the integers. The sequence is followed by a line with the triplet 0 0 0, which marks the end of the input and is not to be processed.

The three integers of a triplet are the integer $m$, the numerator $a$, and the denominator $b$ described above, in this order. It holds that $4 < m < 100000$ and $1 \le a \le b \le 1000$.

Print one line for each input triplet, in the same order. The $i$-th output line answers the $i$-th input triplet and contains the width $p$ and the height $q$ described above, in this order, separated by a single space. Print no other characters.