Neo-Nim

Обмеження: 2 сек., 512 МіБ

There are \(n\) piles of stones. The \(i\)-th pile initially contains \(a_i\) stones. Additionally, an integer \(k\) is given.

Ana and Bob play a game with these stones, alternating turns with Ana going first. The moves are defined as follows.

• Ana chooses an integer \(x\) such that \(2 \le x \le k\) and a pile containing at least \(x\) stones, then removes exactly \(x\) stones from it.

• Bob chooses a pile containing at least one stone and removes exactly one stone from it.

The player who cannot make a move loses. Determine the winner assuming both players play optimally.

Вхідні дані

The first line contains an integer \(t\) – the number of test cases.

The first line of each test case contains two integers \(n\) and \(k\) – the number of piles and the maximum limit for Ana’s move.

The second line of each test case contains \(n\) integers \(a_i\) – the number of stones in each pile.

Вихідні дані

For each test case, output Ana if Ana wins, and Bob if Bob wins.

Обмеження

\(1 \le n \le 10^5\),

\(2 \le k \le 10^5\),

\(1 \le a_i \le 10^5\),

the sum of \(n\) over all test cases does not exceed \(3 \cdot 10^5\).

Приклади

Вхідні дані (stdin) копіювати	Вихідні дані (stdout) копіювати
3 3 2 2 5 8 4 3 2 2 4 5 1 5 2	Bob Bob Ana

Примітки

In the first sample, \(n = 3, k = 2, a = (2, 5, 8)\).

One of the possible game scenarios could be as follows.

• Ana removes two stones from the third pile. After this move \(a\) becomes \((2, 5, 6)\).

• Bob removes one stone from the first pile. After this move \(a\) becomes \((1, 5, 6)\).

• Ana removes two stones from the second pile. After this move \(a\) becomes \((1, 3, 6)\).

• Bob removes one stone from the third pile. After this move \(a\) becomes \((1, 3, 5)\).

• Ana removes two stones from the third pile. After this move \(a\) becomes \((1, 3, 3)\).

• Bob removes one stone from the third pile. After this move \(a\) becomes \((1, 3, 2)\).

• Ana removes two stones from the second pile. After this move \(a\) becomes \((1, 1, 2)\).

• Bob removes one stone from the third pile. After this move \(a\) becomes \((1, 1, 1)\).

• It is Ana’s turn now, but she cannot make a move. Ana loses and Bob wins.

In the first sample, Bob wins.

In the second sample, Bob wins.

In the third sample, Ana wins.