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.*;
import java.lang.*;
import java.math.*;
import java.io.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main{

	Scanner sc=new Scanner(System.in);

	int INF=1<<28;
	double EPS=1e-9;

	int p, m;

	void run(){
		for(;;){
			p=sc.nextInt();
			m=sc.nextInt();
			if((p|m)==0){
				break;
			}
			solve();
		}
	}

	void solve(){
		long n1=0, d1=1;
		long n2=m, d2=1;
		for(long d=1; d<=m; d++){
			double left=1, right=m;
			for(int i=0; i<100; i++){
				double mid=(left+right)/2;
				if(mid*mid<p*d*d+EPS){
					left=mid;
				}else{
					right=mid;
				}
			}
			int n=(int)(left+EPS);
			if(n1*d<n*d1&&n*n<p*d*d){
				n1=n;
				d1=d;
			}
			// debug(n, left,d);
			n++;
			if(p*d*d<n*n&&n*d2<n2*d){}else{
				// debug("error!");
			}

			if(n<=m){
				if(p*d*d<n*n&&n*d2<n2*d){
					n2=n;
					d2=d;
				}
			}
		}
		long gcd=gcd(n2, d2);
		n2/=gcd;
		d2/=gcd;
		gcd=gcd(n1, d1);
		n1/=gcd;
		d1/=gcd;
		println(n2+"/"+d2+" "+n1+"/"+d1);
	}

	long gcd(long m, long n){
		for(; n!=0;){
			m=m%n;
			long t=m;
			m=n;
			n=t;
		}
		return m;
	}

	void debug(Object... os){
		System.err.println(Arrays.deepToString(os));
	}

	void print(String s){
		System.out.print(s);
	}

	void println(String s){
		System.out.println(s);
	}

	public static void main(String[] args){
		// System.setOut(new PrintStream(new BufferedOutputStream(System.out)));
		new Main().run();
	}
}