Problem Statement

There are 2N integers A_1, A_2, ..., A_{2N} written on a blackboard, and an integer M at least 2.
Alice and Bob will play a game.
They will alternately perform the following operation, with Alice going first, until there is no number on the blackboard.

• Choose a number and delete it from the blackboard.

At the end of the game, if the sum of numbers deleted by Alice modulo M equals the sum of numbers deleted by Bob modulo M, Bob wins; otherwise, Alice wins.
Which player will win if both plays optimally?

Input

The input is given from Standard Input in the following format:
N M
$A_1 A_2 \dots A_{2N}$

Output

If Alice wins, print Alice; if Bob wins, print Bob.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $2 \leq M \leq 10^9$
• $0 \leq A_i \leq M - 1$
• All values in the input are integers.

Sample Input 1

2 9
1 4 8 5

Sample Output 1

Alice

The game may proceed as follows.

• Alice deletes 1.
• Bob deletes 4.
• Alice deletes 5.
• Bob deletes 8.

In this case, the sum of numbers deleted by Alice modulo M is $(1 + 5) \bmod 9 = 6$, and the sum of numbers deleted by Bob modulo M is $(4 + 8) \bmod 9 = 3. Since 6 \neq 3,$ Alice wins.

Sample Input 2

3 998244353
1 2 3 1 2 3

Sample Output 2

Bob

见题面 Input 部分

见题面 Output 部分