H. BABA BOOEY
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Alice and Bob take turns playing a game, with Alice going first. Before the first move, there is an array of non-negative integers $$$a_1,a_2,\cdots ,a_n$$$ of length $$$n$$$, along with a positive integer $$$k$$$. In each move, the current player chooses two integers $$$x,y$$$ such that $$$0 \le x \le k$$$, $$$1 \le y \le n$$$, and $$$x \le a_y$$$. Then, $$$k$$$ is updated to $$$x$$$, and $$$a_y$$$ is updated to $$$a_y - x$$$. A player who chooses $$$x = 0$$$ loses immediately. Who has the winning strategy?

Input

There are multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases.

For each test case:

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^6$$$, $$$1 \le k \le 10^9$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 10^9$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases in a single input file does not exceed $$$2\times 10^6$$$.

Output

For each test case, output a single string on a new line.

If the first player (Alice) has a winning strategy for the game described, output "Alice"; otherwise, output "Bob".

Example
Input
3
2 2
1 2
4 5
15 15 8 9
11 2
4 2 9 12 0 15 9 14 5 6 12
Output
Alice
Alice
Bob
Note

In the first test case, the only winning first moves for Alice are $$$(x,y)=(1,1)$$$ and $$$(x,y)=(1,2)$$$.