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Two Pile With Grundy Number

Two players Alice and Bob are playing a game. They have 2 pile's with n1 and n2 coins in it. They can pick only allowed numbers of coins from any one pile at a time given in an array picks. Alice goes first and they take alternate turns. The player who picks the last coin is the winner. Can you find out the winner.

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Two Pile With Grundy Number

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Two players Alice and Bob are playing a game. They have 2 pile's with n1 and n2 coins in it. They can pick only allowed numbers of coins from any one pile at a time given in an array picks. Alice goes first and they take alternate turns. The player who picks the last coin is the winner. Can you find out the winner.

Constraints

1 <= n1, n2 <= 50

Format

Input

The first line contains two integers n1 and n2. Second line contains size of picks array say l picks[0] picks[1] .... picks[l-1]

Output

Print the winner (ALICE or BOB).

Example

Sample Input

4 3 3 1 4 2

Sample Output

BOB

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