Problem:
Score : 300 points

Problem Statement

A game is played on a strip consisting of N cells consecutively numbered from 1 to N.

Alice has her token on cell A. Borys has his token on a different cell B.

Players take turns, Alice moves first.
The moving player must shift his or her token from its current cell X to the neighboring cell on the left, cell X-1, or on the right, cell X+1.
Note that it's disallowed to move the token outside the strip or to the cell with the other player's token.
In one turn, the token of the moving player must be shifted exactly once.

The player who can't make a move loses, and the other player wins.

Both players want to win. Who wins if they play optimally?

Constraints

2 \leq N \leq 100

1 \leq A < B \leq N

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print Alice if Alice wins, Borys if Borys wins, and Draw if nobody wins.

Sample Input 1

5 2 4

Sample Output 1

Alice

Alice can move her token to cell 3.
After that, Borys will be unable to move his token to cell 3, so he will have to move his token to cell 5.
Then, Alice moves her token to cell 4. Borys can't make a move and loses.

Sample Input 2

2 1 2

Sample Output 2

Borys

Alice can't make the very first move and loses.

Sample Input 3

58 23 42

Sample Output 3

Borys

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;   
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;

class Program{

    const long MOD = (long)1e9 + 7;

    static void Main(string[] args)
    {
        // main ↓
        int[] n = ScanIntArray(3);
        Console.WriteLine((int)(Math.Abs(n[2] - n[1])) % 2 == 0 ? "Alice" : "Borys");
        // main↑
    }

    public class SegmentTree<Monoid>
    {
        private bool debug = false;
        // 0-indexed SegmentTree
        public int size;
        Monoid[] segTree;
        Monoid unit;
        public SegmentTree(int inSize, Monoid unit)
        {
            this.unit = unit;
            size = 2;
            while (size < inSize) size *= 2;
            segTree = new Monoid[2 * size];
            for (int i = 0; i < segTree.Length; i++)
            {
                segTree[i] = unit;
                // 単位元なので全部に代入しておけばよい
            }
        }

        public int BinarySearch(int x)
        {
            int high = size;
            int low = 0;
            int mid = (high + low) / 2;
            while (low < high)
            {
                // Console.WriteLine(low + " " + high);
                Monoid cmp = NonRecursiveQuery(0, mid);
                // Console.WriteLine("[ 0, " + mid + " ] -> " + cmp);
                if ((dynamic)cmp >= x)
                {
                    high = mid;
                }
                else if ((dynamic)cmp < x)
                {
                    low = mid + 1;
                }
                mid = (high + low) / 2;
            }
            return mid;
        }

        public void set(int iter, Monoid val)
        {
            segTree[iter + size - 1] = val;
        }

        public Monoid GetMonoid(int index)
        {
            return segTree[index + size - 1];
        }

        public void add(int iter, Monoid val)
        {
            update(iter, (dynamic)segTree[iter + size - 1] + (dynamic)val);
        }

        public void build()
        {
            // 2段目より上の構築
            for (int k = size - 2; k >= 0; k--)
            {
                segTree[k] = F(segTree[2 * k + 1], segTree[2 * k + 2]);
            }
        }

        public Monoid F(Monoid m1, Monoid m2)
        {
            Monoid res = GCD(m1, m2);
            return res;
        }

        public Monoid Query(int ql, int qr, int index, int nl, int nr)
        {
            // Recursive
            // [ql, qr)について考える
            // index に対応する範囲 nl <= x <= nr
            if(nr <= ql || qr <= nl)
            {
                if (debug) Console.WriteLine("Out: [l , r), [" + nl + " ," + nr + "), " + "index: " + index + " ,unit:" + unit);
                return unit;
            }
            if(ql <= nl && nr <= qr)
            {
                if (debug) Console.WriteLine("All in [l , r): [" + nl + " ," + nr + "), " + "index: " + index + ",rangeAns:" + segTree[index]);
                return segTree[index];
            }
            else
            {
                Monoid vl = Query(ql, qr, index * 2 + 1, nl, (nl + nr) / 2);
                Monoid vr = Query(ql, qr, index * 2 + 2, (nl + nr) / 2, nr);
                if (debug) Console.WriteLine("Recursive: [l , r),+: [" + nl + ", " + nr + "), index->"+ index);
                if (debug) Console.WriteLine("(vl, vr): (" + vl + ", " + vr + ")");
                return F(vl, vr);
            }
        }

        public Monoid NonRecursiveQuery(int l,int r)
        {
            // 区間　-> [ l , r ]
            // 非再帰
            int L = l + size - 1;
            int R = r + size - 1;
            Monoid s = unit;
            while (L <= R)
            {
                if(L % 2 == 0)
                {
                    s = F(s, segTree[L]);
                    L++;
                }
                if(R % 2 == 1)
                {
                    s = F(s, segTree[R]);
                }
                L /= 2;
                R /= 2;
                R--;
            }
            return s;
        }

        public void update(int k, Monoid x)
        {
            k += size-1;
            segTree[k] = x;
            while (true)
            {
                k = (k - 1) / 2;
                segTree[k] = F(segTree[k * 2 + 1], segTree[k * 2 + 2]);
                if(k == 0)
                {
                    break;
                }
            }
        }

        public void print()
        {
            Console.Write("Print:");
            for (int i = 0; i < segTree.Length; i++)
            {
                Console.Write(segTree[i] + " ");
            }
            Console.WriteLine("");
        }

    }

    static int Nibutan(long[] array, long k)
    {
        int low = 0 ;
        int high = array.Length-1;
        int mid = high;

        while (low < high)
        {
            mid = (low + high) / 2;
            if(array[mid] >= k) // k以上の最小index.ココを変えるだけ
            {
                high = mid;
            }
            else
            {
                low = mid + 1;
            }
            mid = (low + high) / 2;
        }
        return mid;
    }   

    static int ScanOneInt()
    {
        return int.Parse(Console.ReadLine());
    }

    static long ScanOneLong()
    {
        return long.Parse(Console.ReadLine());
    }

    static string[] ScanStringArray(int lines)
    {
        string[] str = new string[lines];
        for (int i = 0; i < lines; i++)
        {
            str[i] = Console.ReadLine();
        }
        return str;
    }

    static int[] ScanIntArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] ar = new int[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = int.Parse(str[i]);
        }
        return ar;
    }

    static string[] ScanStringArrayInOneLine(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        return str;
    }

    static Tuple<int,int> ScanTuple()
    {
        int[] tmp = ScanIntArray(2);
        return new Tuple<int, int>(tmp[0], tmp[1] * -1);
    }

    static long[] ScanLongArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        long[] ar = new long[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = long.Parse(str[i]);
        }
        return ar;
    }

    static double[] ScanDoubleArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        double[] ar = new double[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = double.Parse(str[i]);
        }
        return ar;
    }

    static int[,] ScanIntSquareArray(int h, int w)
    {
        int[,] resAr = new int[h, w];
        for (int i = 0; i < h; i++)
        {
            int[] ar = ScanIntArray(w);
            for (int j = 0; j < w; j++)
            {
                resAr[i, j] = ar[j];
            }
        }
        return resAr;
    }

    static int[,] CombModMake()
    {
        int[,] res = new int[2005, 2005];
        for (int i = 0; i < 2005; i++)
        {
            for (int j = 0; j < 2005; j++)
            {
                if (i == 0 || i < j)
                {
                    res[i, j] = 0;
                }
                else if (j == 0 || i == j)
                {
                    res[i, j] = 1;
                }
                else
                {
                    res[i, j] = (res[i - 1, j] + res[i - 1, j - 1]) % (int)MOD;
                }
            }
        }
        return res;
    }

    // int, long両方で出来るGCDを作った
    static T GCD<T>(T a, T b)
    {
        if((dynamic)b == 0)
        {
            return a;
        }
        else
        {
            return GCD((dynamic)b, (dynamic)a % (dynamic)b);
        }
    }

    static bool isPrime(int a) //O(sqrt N)
    {
        int max = (int)Math.Sqrt(a);
        if (a == 1) return false;
        for (int i = 2; i <= max; i++)
        {
            if(a % i == 0)
            {
                return false;
            }
        }
        return true;
    }
}

public class Pair<T,U>: IComparable where T : IComparable<T> where U: IComparable<U>
{
    public T Item1;
    public U Item2;

    public int  CompareTo(object obj)
    {
        Pair<T,U> pair = (Pair<T, U>)obj;
        return Item1.CompareTo(pair.Item1);
    }
    public Pair(T t, U u)
    {
        Item1 = t;
        Item2 = u;
    }

}

// 計算量: Push -> O(logN), Peek -> O(1)。Clear() -> O(logN)
// ToArray()で配列化
public class PriorityQueue<T> where T : IComparable
{
    private IComparer<T> _comparer = null;
    private int _type = 0;
    private T[] _heap;
    private int _sz = 0;
    private int _count = 0;

    /// <summary>
    /// Priority Queue with custom comparer
    /// </summary>
    public PriorityQueue(int maxSize, IComparer<T> comparer)
    {
        _heap = new T[maxSize];
        _comparer = comparer;
    }

    /*
     -> Item: _heap(ヒープを持つ.sizeはmaxSize)
     -> Item: _type -> 0:asc(昇順), 1:desc(降順)
     */
    public PriorityQueue(int maxSize, int type = 0)
    {
        _heap = new T[maxSize];
        _type = type;
    }

    private int Compare(T x, T y)
    {
        if (_comparer != null) return _comparer.Compare(x, y);
        return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        // typeが0なら昇順, 1なら降順にソートするCompare
    }

    public void Push(T x)
    {
        _count++;

        //node number
        var i = _sz++;

        while (i > 0)
        {
            //parent node number
            var p = (i - 1) / 2;
            if (Compare(_heap[p], x) <= 0) break;
            _heap[i] = _heap[p];
            i = p;
        }

        _heap[i] = x;
    }

    public T Pop()
    {
        _count--;

        T ret = _heap[0];
        T x = _heap[--_sz];

        int i = 0;
        while (i * 2 + 1 < _sz)
        {
            //children
            int a = i * 2 + 1;
            int b = i * 2 + 2;

            if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

            if (Compare(_heap[a], x) >= 0) break;

            _heap[i] = _heap[a];
            i = a;
        }

        _heap[i] = x;

        return ret;
    }

    public int Count()  // O(1)
    {
        return _count;
    }

    public T Peek() // O(1)
    {
        return _heap[0];
    }

    public bool Contains(T x)   // O(N)なので注意
    {
        for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
        return false;
    }

    public void Clear()
    {
        while (Count() > 0) Pop();
    }

    public IEnumerator<T> GetEnumerator() // なにこれ
    {
        var ret = new List<T>();

        while (Count() > 0)
        {
            ret.Add(Pop());
        }

        foreach (var r in ret)
        {
            Push(r);
            yield return r;
        }
    }

    public T[] ToArray()
    {
        T[] array = new T[_sz];
        int i = 0;

        foreach (var r in this)
        {
            array[i++] = r;
        }

        return array;
    }
}

public class GenericOperation<T>
{
    public GenericOperation()
    {
        var availableT = new Type[]
        {
            typeof(int), typeof(uint), typeof(short), typeof(ushort), typeof(long), typeof(ulong), typeof(byte),
            typeof(decimal), typeof(double)
        };
        if (!availableT.Contains(typeof(T)))
        {
            throw new NotSupportedException();
        }
        var p1 = Expression.Parameter(typeof(T));
        var p2 = Expression.Parameter(typeof(T));
        Add = Expression.Lambda<Func<T, T, T>>(Expression.Add(p1, p2), p1, p2).Compile();
        Subtract = Expression.Lambda<Func<T, T, T>>(Expression.Subtract(p1, p2), p1, p2).Compile();
        Multiply = Expression.Lambda<Func<T, T, T>>(Expression.Multiply(p1, p2), p1, p2).Compile();
        Divide = Expression.Lambda<Func<T, T, T>>(Expression.Divide(p1, p2), p1, p2).Compile();
        Modulo = Expression.Lambda<Func<T, T, T>>(Expression.Modulo(p1, p2), p1, p2).Compile();
        Equal = Expression.Lambda<Func<T, T, bool>>(Expression.Equal(p1, p2), p1, p2).Compile();
        GreaterThan = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThan(p1, p2), p1, p2).Compile();
        GreaterThanOrEqual = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThanOrEqual(p1, p2), p1, p2).Compile();
        LessThan = Expression.Lambda<Func<T, T, bool>>(Expression.LessThan(p1, p2), p1, p2).Compile();
        LessThanOrEqual = Expression.Lambda<Func<T, T, bool>>(Expression.LessThanOrEqual(p1, p2), p1, p2).Compile();
    }

    public Func<T, T, T> Add { get; private set; }
    public Func<T, T, T> Subtract { get; private set; }
    public Func<T, T, T> Multiply { get; private set; }
    public Func<T, T, T> Divide { get; private set; }
    public Func<T, T, T> Modulo { get; private set; }
    public Func<T, T, bool> Equal { get; private set; }
    public Func<T, T, bool> GreaterThan { get; private set; }
    public Func<T, T, bool> GreaterThanOrEqual { get; private set; }
    public Func<T, T, bool> LessThan { get; private set; }
    public Func<T, T, bool> LessThanOrEqual { get; private set; }
}