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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
	"strings"
)

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func init() {
	ReadString = newReadString(os.Stdin)
	stdout = bufio.NewWriter(os.Stdout)
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	// Split sets the split function for the Scanner. The default split function is ScanLines.
	// Split panics if it is called after scanning has started.
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** DP sub-functions ***********/

// ChMin accepts a pointer of integer and a target value.
// If target value is SMALLER than the first argument,
//	then the first argument will be updated by the second argument.
func ChMin(updatedValue *int, target int) bool {
	if *updatedValue > target {
		*updatedValue = target
		return true
	}
	return false
}

// ChMax accepts a pointer of integer and a target value.
// If target value is LARGER than the first argument,
//	then the first argument will be updated by the second argument.
func ChMax(updatedValue *int, target int) bool {
	if *updatedValue < target {
		*updatedValue = target
		return true
	}
	return false
}

// GetNthBit returns nth bit value of an argument.
// n starts from 0.
func GetNthBit(num, nth int) int {
	return num >> uint(nth) & 1
}

/*********** Arithmetic ***********/

// Max returns the max integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Max(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m < integer {
			m = integer
		}
	}
	return m
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// CeilInt returns the minimum integer larger than or equal to float(a/b).
func CeilInt(a, b int) int {
	res := a / b
	if a%b > 0 {
		res++
	}
	return res
}

// FloorInt returns the maximum integer smaller than or equal to float(a/b)
func FloorInt(a, b int) int {
	res := a / b
	return res
}

// PowInt is integer version of math.Pow
// PowInt calculate a power by Binary Power (二分累乗法(O(log e))).
func PowInt(a, e int) int {
	if a < 0 || e < 0 {
		panic(errors.New("[argument error]: PowInt does not accept negative integers"))
	}

	if e == 0 {
		return 1
	}

	if e%2 == 0 {
		halfE := e / 2
		half := PowInt(a, halfE)
		return half * half
	}

	return a * PowInt(a, e-1)
}

// AbsInt is integer version of math.Abs
func AbsInt(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// Gcd returns the Greatest Common Divisor of two natural numbers.
// Gcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Gcd uses the Euclidean Algorithm.
func Gcd(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}
	if a < b {
		a, b = b, a
	}

	// Euclidean Algorithm
	for b > 0 {
		div := a % b
		a, b = b, div
	}

	return a
}

// Lcm returns the Least Common Multiple of two natural numbers.
// Lcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Lcd uses the Euclidean Algorithm indirectly.
func Lcm(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}

	// a = a'*gcd, b = b'*gcd, a*b = a'*b'*gcd^2
	// a' and b' are relatively prime numbers
	// gcd consists of prime numbers, that are included in a and b
	gcd := Gcd(a, b)

	// not (a * b / gcd), because of reducing a probability of overflow
	return (a / gcd) * b
}

/*********** Utilities ***********/

// DeleteElement returns a *NEW* slice, that have the same and minimum length and capacity.
// DeleteElement makes a new slice by using easy slice literal.
func DeleteElement(s []int, i int) []int {
	if i < 0 || len(s) <= i {
		panic(errors.New("[index error]"))
	}
	// appendのみの実装
	n := make([]int, 0, len(s)-1)
	n = append(n, s[:i]...)
	n = append(n, s[i+1:]...)
	return n
}

// Concat returns a *NEW* slice, that have the same and minimum length and capacity.
func Concat(s, t []rune) []rune {
	n := make([]rune, 0, len(s)+len(t))
	n = append(n, s...)
	n = append(n, t...)
	return n
}

// UpperRune is rune version of `strings.ToUpper()`.
func UpperRune(r rune) rune {
	str := strings.ToUpper(string(r))
	return []rune(str)[0]
}

// LowerRune is rune version of `strings.ToLower()`.
func LowerRune(r rune) rune {
	str := strings.ToLower(string(r))
	return []rune(str)[0]
}

// ToggleRune returns a upper case if an input is a lower case, v.v.
func ToggleRune(r rune) rune {
	var str string
	if 'a' <= r && r <= 'z' {
		str = strings.ToUpper(string(r))
	} else if 'A' <= r && r <= 'Z' {
		str = strings.ToLower(string(r))
	} else {
		str = string(r)
	}
	return []rune(str)[0]
}

// ToggleString iteratively calls ToggleRune, and returns the toggled string.
func ToggleString(s string) string {
	inputRunes := []rune(s)
	outputRunes := make([]rune, 0, len(inputRunes))
	for _, r := range inputRunes {
		outputRunes = append(outputRunes, ToggleRune(r))
	}
	return string(outputRunes)
}

// Strtoi is a wrapper of `strconv.Atoi()`.
// If `strconv.Atoi()` returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

/*********** Permutation ***********/

// memo: 10! == 3628800 > 3M
func CalcFactorialPatterns(elements []rune) [][]rune {
	copiedResidual := make([]rune, len(elements))
	copy(copiedResidual, elements)
	return factorialRecursion([]rune{}, copiedResidual)
}
func factorialRecursion(interim, residual []rune) [][]rune {
	if len(residual) == 0 {
		return [][]rune{interim}
	}

	res := [][]rune{}
	for idx, elem := range residual {
		copiedInterim := make([]rune, len(interim))
		copy(copiedInterim, interim)
		copiedInterim = append(copiedInterim, elem)
		copiedResidual := genDeletedSlice(idx, residual)
		res = append(res, factorialRecursion(copiedInterim, copiedResidual)...)
	}

	return res
}
func genDeletedSlice(delId int, S []rune) []rune {
	res := []rune{}
	res = append(res, S[:delId]...)
	res = append(res, S[delId+1:]...)
	return res
}

// memo: 3**10 == 59049
func CalcDuplicatePatterns(elements []rune, digit int) [][]rune {
	return duplicateRecursion([]rune{}, elements, digit)
}
func duplicateRecursion(interim, elements []rune, digit int) [][]rune {
	if len(interim) == digit {
		return [][]rune{interim}
	}

	res := [][]rune{}
	for i := 0; i < len(elements); i++ {
		copiedInterim := make([]rune, len(interim))
		copy(copiedInterim, interim)
		copiedInterim = append(copiedInterim, elements[i])
		res = append(res, duplicateRecursion(copiedInterim, elements, digit)...)
	}

	return res
}

// usage
//tmp := CalcFactorialPatterns([]rune{'a', 'b', 'c'})
//expected := []string{"abc", "acb", "bac", "bca", "cab", "cba"}
//tmp := CalcDuplicatePatterns([]rune{'a', 'b', 'c'}, 3)
//expected := []string{"aaa", "aab", "aac", "aba", "abb", "abc", ...}

/*********** Binary Search ***********/

func GeneralLowerBound(s []int, key int) int {
	isOK := func(index, key int) bool {
		if s[index] >= key {
			return true
		}
		return false
	}

	ng, ok := -1, len(s)
	for int(math.Abs(float64(ok-ng))) > 1 {
		mid := (ok + ng) / 2
		if isOK(mid, key) {
			ok = mid
		} else {
			ng = mid
		}
	}

	return ok
}

func GeneralUpperBound(s []int, key int) int {
	isOK := func(index, key int) bool {
		if s[index] > key {
			return true
		}
		return false
	}

	ng, ok := -1, len(s)
	for int(math.Abs(float64(ok-ng))) > 1 {
		mid := (ok + ng) / 2
		if isOK(mid, key) {
			ok = mid
		} else {
			ng = mid
		}
	}

	return ok
}

// usage
//test := []int{1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 10, 10, 10, 20, 20, 20, 30, 30, 30}
//assert.Equal(t, 5, GeneralUpperBound(test, 5)-GeneralLowerBound(test, 5))
//assert.Equal(t, 0, GeneralUpperBound(test, 15)-GeneralLowerBound(test, 15))

/*********** Union Find ***********/

func InitParents(parents []int, maxNodeId int) {
	for i := 0; i <= maxNodeId; i++ {
		parents[i] = i
	}
}

func unite(x, y int, parents []int) {
	xp, yp := root(x, parents), root(y, parents)
	if xp == yp {
		return
	}

	parents[xp] = yp
}

func same(x, y int, parents []int) bool {
	return root(x, parents) == root(y, parents)
}

func root(x int, parents []int) int {
	if parents[x] == x {
		return x
	}

	parents[x] = root(parents[x], parents)
	return parents[x]
}

/*********** Factorization, Prime Number ***********/

// TrialDivision returns the result of prime factorization of integer N.
// Complicity: O(n)
func TrialDivision(n int) map[int]int {
	if n <= 1 {
		panic(errors.New("[argument error]: TrialDivision only accepts a NATURAL number"))
	}

	p := map[int]int{}
	for i := 2; i*i <= n; i++ {
		exp := 0
		for n%i == 0 {
			exp++
			n /= i
		}

		if exp == 0 {
			continue
		}
		p[i] = exp
	}
	if n > 1 {
		p[n] = 1
	}

	return p
}

// IsPrime judges whether an argument integer is a prime number or not.
func IsPrime(n int) bool {
	if n == 1 {
		return false
	}

	for i := 2; i*i <= n; i++ {
		if n%i == 0 {
			return false
		}
	}

	return true
}

/*********** Inverse Element ***********/

// CalcNegativeMod can calculate a right residual whether value is positive or negative.
func CalcNegativeMod(val, m int) int {
	res := val % m
	if res < 0 {
		res += m
	}
	return res
}

func modpow(a, e, m int) int {
	if e == 0 {
		return 1
	}

	if e%2 == 0 {
		halfE := e / 2
		half := modpow(a, halfE, m)
		return half * half % m
	}

	return a * modpow(a, e-1, m) % m
}

// CalcModInv returns $a^{-1} mod m$ by Fermat's little theorem.
// O(1), but C is nearly equal to 30 (when m is 1000000000+7).
func CalcModInv(a, m int) int {
	return modpow(a, m-2, m)
}

/********** heap package (Integer Priority Queue) **********/

type IntHeap []int

func (h IntHeap) Len() int           { return len(h) }
func (h IntHeap) Less(i, j int) bool { return h[i] < h[j] }
func (h IntHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *IntHeap) Push(x interface{}) {
	*h = append(*h, x.(int))
}
func (h *IntHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

// h := &IntHeap{3, 6, 1, 2}
// heap.Init(h)
// heap.Push(h, followers[i])
// poppedD := heap.Pop(h).(int)

/********** sort package (snippets) **********/
//sort.Sort(sort.IntSlice(s))
//sort.Sort(sort.Reverse(sort.IntSlice(s)))
//sort.Sort(sort.Float64Slice(s))
//sort.Sort(sort.StringSlice(s))

// struct sort
type Mono struct {
	key, value int
}
type MonoList []*Mono

func (ml MonoList) Len() int {
	return len(ml)
}
func (ml MonoList) Swap(i, j int) {
	ml[i], ml[j] = ml[j], ml[i]
}
func (ml MonoList) Less(i, j int) bool {
	return ml[i].value < ml[j].value
}

// Example(ABC111::C)
//oddCountList, evenCountList := make(MonoList, 1e5+1), make(MonoList, 1e5+1)
//for i := 0; i <= 1e5; i++ {
//	oddCountList[i] = &Mono{key: i, value: oddMemo[i]}
//	evenCountList[i] = &Mono{key: i, value: evenMemo[i]}
//}
//sort.Sort(sort.Reverse(oddCountList))		// DESC sort
//sort.Sort(sort.Reverse(evenCountList))	// DESC sort

/********** copy function (snippets) **********/
//a = []int{0, 1, 2}
//b = make([]int, len(a))
//copy(b, a)

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()

/********** String Split **********/

//strs := strings.Split(string(runeSlice), "+")

/*******************************************************************/

const MOD = 1000000000 + 7
const ALPHABET_NUM = 26

var n, a, b int

func main() {
	n, a, b = ReadInt(), ReadInt(), ReadInt()

	if (b-a)%2 == 0 {
		fmt.Println("Alice")
	} else {
		fmt.Println("Borys")
	}
}