/*
 * UnitFraction : 
 *     Accept input from the user a fraction between 0 and 1 (non-inclusive).
 *     Find a decomposition of the fraction into a sum of unit fractions.
 *     A unit fraction simply is a fraction with a numerator of one.
 *
 *     Interestingly, there always exists such a (finite) sum of unit
 *     fractions that is equivalent to any given fraction.
 *
 *     E.g., 5/6   = 1/2 + 1/3
 *           13/87 = 1/7 + 1/153 + 1/31059.
 *
 *     The decomposition into unit fractions is not necessarily unique.
 *     That is, there may be several different sums that work.
 *
 *     One algorithm that will always find us a unit fraction sum
 *     for our fraction is by Fibonacci.
 *       * Find the largest unit fraction (so smallest denominator) that
 *         is smaller than, or equal to our fraction.
 *       * Print out this unit fraction.
 *       * Subtract it from our fraction.
 *       * If our fraction is now zero, we are done!
 *         Otherwise, repeat the process.
 *
 *     This is guaranteed to finish.
 *
 * Parke Godfrey
 * 2009 October 20
*/

import java.io.PrintStream;
import java.util.Scanner;
import type.lib.Fraction;

public class UnitFractionA {
    public static void main(String[] useless)
    {
        Scanner input = new Scanner(System.in);
        PrintStream output = System.out;
        
        output.println("Enter a positive fraction "
                    + "(numerator denominator):");
        Fraction frac = new Fraction(input.nextLong(),
                                    input.nextLong());
        boolean first = true;
        // While not zero...
        while (!frac.equals(new Fraction(0, 1))) 
        {
            // Find the largest unit fraction smaller than, or equal to,
            // frac.  One way to do this is to start with 1/2.  If too big,
            // then consider 1/3.  Still too big, then 1/4.  And so on.
            Fraction unit = new Fraction(1, 2);
            while (unit.compareTo(frac) > 0)
            {
                unit = new Fraction(1, unit.getDenominator() + 1);
            }

            // Do not print a leading "+" the first time through.
            if (first)
            {
                first = false;
            } else
            {
                output.print(" + ");
            }
            output.print(unit);
            
            frac.subtract(unit);
        }
        output.println(".");
    }
}