下面给出两道POJ上的问题，看如何用穷举法解决。

【例9】Calling Extraterrestrial Intelligence Again（POJ 1411）

Description

A message from humans to extraterrestrial intelligence was sent through the Arecibo radio telescope in Puerto Rico on the afternoon of Saturday November 16, 1974. The message consisted of 1679 bits and was meant to be translated to a rectangular picture with 23 x 73 pixels. Since both 23 and 73 are prime numbers, 23 x 73 is the unique possible size of the translated rectangular picture each edge of which is longer than 1 pixel. Of course, there was no guarantee that the receivers would try to translate the message to a rectangular picture. Even if they would, they might put 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 translated rectangular picture. The term "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 should not be greater than m. Both of the width and the height of the translated picture should be prime numbers. The ratio of the width to the height should not be less than a/b nor greater than 1. You should maximize the area of the picture under these constraints.

In other words, you will receive an integer m and a fraction a/b. It holds that m > 4 and 0 < a/b <= 1. You should find the pair of prime numbers p, q such that pq <= m and a/b <= p/q <= 1, and furthermore, the product pq takes the maximum value among such pairs of two prime numbers. You should report p and q as the "most suitable" width and height of the translated picture.

Input

The input is a sequence of at most 2000 triplets of positive integers, delimited by a space character in between. Each line contains a single triplet. The sequence is followed by a triplet of zeros, 0 0 0, which indicates the end of the input and should not be treated as data to be processed.

The integers of each input triplet are the integer m, the numerator a, and the denominator b described above, in this order. You may assume 4 < m <= 100000 and 1 <= a <= b <= 1000.

Output

The output is a sequence of pairs of positive integers. The i-th output pair corresponds to the i-th input triplet. The integers of each output pair are the width p and the height q described above, in this order.

Each output line contains a single pair. A space character is put between the integers as a delimiter. No other characters should appear in the output.

Sample Input

5 1 2

99999 999 999

1680 5 16

1970 1 1

2002 4 11

0 0 0

Sample Output

2 2

313 313

23 73

43 43

37 53

      （1）编程思路。

      对于输入的m，通过穷举找到一组质数对（p，q），满足条件：1）p、q均为质数，且p<=q<=m；2）p*q<=m；3）a/b <= p/q；4）p*q取得最大值。

      首先确定p和q的穷举范围，由于m不超过100000，因此p和q不会超过50000（因为最小的质数为2，2*50000=100000）。进一步考虑，由于1<=a<=b<=1000，所以a/b的最小值为1/1000=0.001，因此，p/q>=0.001。而当m达到最大100000时，100000/11=9090.9，质数2、3、5、7除以9091均小于0.001，因此，可将p、q的范围进一步缩小到取2~9091之间的质数。

      先将小于9092的所有质数求出来，并存放在数组prime中，记下质数的个数num。

      用二重循环穷举所有的p（prime[0]~prime[num-1]）、q（p~prime[num-1]）组合，对每种组合去判断是否符合条件，如果满足，将p*q与当前最大值max比较，保存最大的p*q。

      （2）源程序。

#include <iostream>

using namespace std;

int main()

{

    int flag[9092]={0},prime[5000]={0};