Aklank
Tag(s):

## Easy-Medium

Problem
Editorial
Analytics

Aklank has a habit of challenging his friends in different games. But every time he fails to defeat them and gets frustrated. So, this time he devised one game and named it "Bakkund". Bakkund is played between two players. Initially there will be N integers. In each turn one player can select any of the n integer and divide it either by a or b either once or more than one times. He can choose to continue until it is divisible by either a or b.

Suppose an integer is 6 and a = 2 and b=3: Possible moves are :

1) 6/2 = 3

2) 6/3 =2

3) 6/2 = 3, 3/3 =1

4) 6/3 = 2, 2/2 =1

If in a particular turn a player is not able to take any move than he loses.

Assume that each time Aklank will start first and both will play optimally. Predict whether Aklank can win the game.

Input

First line will contain three space separated integers N, a and b.

Next line contains N space separated integers Ai.

Output

Print "Aklank's day" if Aklank wins else print "Bad Luck".

Constraint

2 ≤ N, a, b ≤ 100000

1 ≤ Ai ≤ 100000

Setter : Sourav Kumar Paul

SAMPLE INPUT
3 2 3
2 4 6
SAMPLE OUTPUT
Aklank's day
Explanation

2, 4, 6

Optimal moves are :

1) Aklank : 2/2 -> 1

Status of numbers are : 1, 4, 6

2) Friend : 4/2 -> 2

Status : 1, 2, 6

3) Aklank : 6/3 -> 2

Status : 1, 2, 2

4) Friend : 2/2 -> 1

Status : 1, 1, 2

5) Aklank : 2/2 -> 1

No move left for his friend. So, Aklank wins.

Time Limit: 5.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, Visual Basic

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