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: Accepted)

import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {

	static Scanner sc = new Scanner(System.in);
	static int P, N;

	public static void main(String[] args) {
		while (true) {
			P = sc.nextInt();
			N = sc.nextInt();
			if (N == 0) break;
			ArrayList<Rational> low = new ArrayList<Rational>();
			ArrayList<Rational> high = new ArrayList<Rational>();
			for (long den = 1; den <= N; ++den) {
				double numf = Math.sqrt(den * den * P);
				long lo = (long) numf;
				if (lo <= N && gcd(lo, den) == 1) {
					low.add(new Rational(lo, den));
				}
				long hi = lo + 1;
				if (hi <= N && gcd(hi, den) == 1) {
					high.add(new Rational(hi, den));
				}
			}
			Collections.sort(low);
			Collections.sort(high);
			Rational l = low.get(low.size() - 1);
			Rational r = high.get(0);
			System.out.printf("%d/%d %d/%d\n", r.num, r.den, l.num, l.den);
		}
	}

	static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	static class Rational implements Comparable<Rational> {
		long num, den;

		Rational(long n, long d) {
			num = n;
			den = d;
		}

		public int compareTo(Rational o) {
			long v1 = num * o.den;
			long v2 = den * o.num;
			if (v1 < v2) return -1;
			if (v1 > v2) return 1;
			return 0;
		}

	}

}