Cougarettes Contest 1

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2020-07-25 09:00 AKDT

Cougarettes Contest 1

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2020-07-25 11:00 AKDT
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Problem E
Multiplication Game

Alice and Bob are in their class doing drills on multiplication and division. They quickly get bored and instead decide to play a game they invented.

The game starts with a target integer $N \geq 2$, and an integer $M = 1$. Alice and Bob take alternate turns. At each turn, the player chooses a prime divisor $p$ of $N$, and multiply $M$ by $p$. If the player’s move makes the value of $M$ equal to the target $N$, the player wins. If $M > N$, the game is a tie.

Assuming that both players play optimally, who (if any) is going to win?

Input

The first line of input contains $T$ ($1 \leq T \leq 10\, 000$), the number of cases to follow. Each of the next $T$ lines describe a case. Each case is specified by $N$ ($2 \leq N \leq 2^{31}-1$) followed by the name of the player making the first turn. The name is either Alice or Bob.

Output

For each case, print the name of the winner (Alice or Bob) assuming optimal play, or tie if there is no winner.

Sample Input 1 Sample Output 1
10
10 Alice
20 Bob
30 Alice
40 Bob
50 Alice
60 Bob
70 Alice
80 Bob
90 Alice
100 Bob
Bob
Bob
tie
tie
Alice
tie
tie
tie
tie
Alice