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.Scanner;

class Main {
    private static int gcd(int a, int b) {
        if (a % b == 0) {
            return b;
        } else {
            return gcd(b, a % b);
        }
    }

    private static void solve() {
        Scanner scanner = new Scanner(System.in);

        while (true) {
            int p = scanner.nextInt();
            int n = scanner.nextInt();
            if (p == 0 && n == 0) {
                break;
            }
            int u = 1;
            int v = n;
            int x = n;
            int y = 1;

            for (int i = 1; i <= n; i++) {
                int num = (int) (i * Math.sqrt(p));
                int den = i;
                if (num > n) {
                    break;
                }
                if ((double) num / den > (double) u / v && gcd(num, den) == 1) {
                    u = num;
                    v = den;
                }
                num++;
                if (num > n) {
                    continue;
                }
                if ((double) num / den < (double) x / y && gcd(num, den) == 1) {
                    x = num;
                    y = den;
                }
            }
            System.out.println(String.format("%d/%d %d/%d", x, y, u, v));
        }
    }

    public static void main(String... args) {
        solve();
    }
}