using System;

​

public class Program {

    private interface ITerm {

        int Item1 { get; }

        int Item2 { get; }

        int Item3 { get; }

    }

    private class Term : ITerm {

        public Term(int item1, int item2, int item3) {

            this.Item1 = item1;

            this.Item2 = item2;

            this.Item3 = item3;

        }

        public int Item1 { get; private set; }

        public int Item2 { get; private set; }

        public int Item3 { get; private set; }

    }

    private interface ITermPrinter {

        void Print(ITerm term); 

    }

    private class TermPrinter : ITermPrinter {

        public void Print(ITerm term) {

            if (term.Item1 != 1) {

                Console.Out.Write(term.Item1);

            }

            Print("x", term.Item2);

            Print("y", term.Item3);

        }

        private void Print(string s, int i) {

            if (i != 0) {

                Console.Out.Write(s);

                if (i != 1) {

                    Console.Out.Write("^" + i);

                }

            }

        }

    }

    private interface ITermsPrinter {

        void Print(ITerm[] terms);

    }

    private class TermsPrinter : ITermsPrinter {

        private ITermPrinter termPrinter;

        public TermsPrinter(ITermPrinter termPrinter) {

            if (termPrinter == null) {

                throw new ArgumentNullException("termPrinter");

            }

            this.termPrinter = termPrinter;

        }

        public void Print(ITerm[] terms) {

            termPrinter.Print(terms[0]);

            for (int i = 1; i < terms.Length; i++) {

                Console.Out.Write(" + ");

                termPrinter.Print(terms[i]);

            }

            Console.Out.WriteLine();

        }

    }

    private interface ITermFactory {

        ITerm Create(int item1, int item2, int item3);

    }

    private class TermFactory : ITermFactory {

        public ITerm Create(int item1, int item2, int item3) {

            return new Term(item1, item2, item3);

        }

    }

    public static void Main() {

        new Program(new TermsPrinter(new TermPrinter()), new TermFactory()).Start();

    }

    private ITermsPrinter termsPrinter;

    private ITermFactory termFactory;

    private Program(ITermsPrinter termsPrinter, ITermFactory termFactory) {     

        if (termsPrinter == null) {

            throw new ArgumentNullException("termsPrinter");

        }

        if (termFactory == null) {

            throw new ArgumentNullException("termFactory");

        }

        this.termsPrinter = termsPrinter;

        this.termFactory = termFactory;

    }

    private void Start() {

        for (int i = 2; i <= 16; i += 2) {

            this.termsPrinter.Print(this.TermShizzle(i));

        }

    }

    private ITerm[] TermShizzle(int power) {

        ITerm[] terms = new ITerm[power + 1];

        terms[0] = this.termFactory.Create(1, power, 0);

        int i = 1;

        int j = 1;

        for (int l = power / 2; j <= l; j++) {          

            i = (int) ((double) (power-j+1) / j * i);

            terms[j] = this.termFactory.Create(i, power - j, j);

        }

        for (; j <= power; j++) {

            terms[j] = this.termFactory.Create(terms[power - j].Item1, power - j, j);

        }

        return terms;

    }

}