Problem:
Problem A: Rational Irrationals

Rational numbers are numbers represented by ratios of two integers. For a prime number p, one of the elementary theorems in the number theory is that there is no rational number equal to √p. Such numbers are called irrational numbers. It is also known that there are rational numbers arbitrarily close to √p

Now, given a positive integer n, we define a set Qn of all rational numbers whose elements are represented by ratios of two positive integers both of which are less than or equal to n. For example, Q4 is a set of 11 rational numbers {1/1, 1/2, 1/3, 1/4, 2/1, 2/3, 3/1, 3/2, 3/4, 4/1, 4/3}. 2/2, 2/4, 3/3, 4/2 and 4/4 are not included here because they are equal to 1/1, 1/2, 1/1, 2/1 and 1/1, respectively.

Your job is to write a program that reads two integers p and n and reports two rational numbers x / y and u / v, where u / v < √p < x / y and there are no other elements of Qn between u/v and x/y. When n is greater than √p, such a pair of rational numbers always exists.

Input

The input consists of lines each of which contains two positive integers, a prime number p and an integer n in the following format.

p n

They are separated by a space character. You can assume that p and n are less than 10000, and that n is greater than √p. The end of the input is indicated by a line consisting of two zeros.

Output

For each input line, your program should output a line consisting of the two rational numbers x / y and u / v (x / y > u / v) separated by a space character in the following format.

x/y u/v

They should be irreducible. For example, 6/14 and 15/3 are not accepted. They should be reduced to 3/7 and 5/1, respectively.

Sample Input

2 5
3 10
5 100
0 0

Output for the Sample Input

3/2 4/3
7/4 5/3
85/38 38/17

Solution in JAVA (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	final int INF = 1 << 28;

	void run() {
		Scanner sc = new Scanner(System.in);
		while (true) {
			int p = sc.nextInt();
			int n = sc.nextInt();
			if ((p | n) == 0)
				break;
			double max = 0;
			double min = Double.POSITIVE_INFINITY;
			double rp = Math.sqrt(p);
			int a = 1;
			int b = 1;
			int u = 0;
			int v = 0;
			int x = 0;
			int y = 0;
			while (true) {
				if (1.0 * a / b > rp) {
					if (min > 1.0 * a / b) {
						min = 1.0 * a / b;
						x = a;
						y = b;
					}
					b++;
					if (a > n)
						break;
				} else {
					if (max < 1.0 * a / b) {
						max = 1.0 * a / b;
						u = a;
						v = b;
					}
					a++;
					if (b > n)
						break;
				}
			}
			int g1 = gcd(x, y);
			int g2 = gcd(u, v);
			x /= g1;
			y /= g1;
			u /= g2;
			v /= g2;
			System.out.println(x + "/" + y + " " + u + "/" + v);
		}
	}

	int gcd(int a, int b) {
		if (a < b) {
			a = a ^ b;
			b = a ^ b;
			a = a ^ b;
		}
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}
}