Codeforces Round 941 (Div. 1) |
---|
Finished |
Alice and Bob are playing a game on $$$n$$$ piles of stones. On each player's turn, they select a positive integer $$$k$$$ that is at most the size of the smallest nonempty pile and remove $$$k$$$ stones from each nonempty pile at once. The first player who is unable to make a move (because all piles are empty) loses.
Given that Alice goes first, who will win the game if both players play optimally?
The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2\cdot 10^5$$$) — the number of piles in the game.
The next line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots a_n$$$ ($$$1 \le a_i \le 10^9$$$), where $$$a_i$$$ is the initial number of stones in the $$$i$$$-th pile.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.
For each test case, print a single line with the name of the winner, assuming both players play optimally. If Alice wins, print "Alice", otherwise print "Bob" (without quotes).
753 3 3 3 321 771 3 9 7 4 2 10031 2 362 1 3 4 2 485 7 2 9 6 3 3 211000000000
Alice Bob Alice Alice Bob Alice Alice
In the first test case, Alice can win by choosing $$$k=3$$$ on her first turn, which will empty all of the piles at once.
In the second test case, Alice must choose $$$k=1$$$ on her first turn since there is a pile of size $$$1$$$, so Bob can win on the next turn by choosing $$$k=6$$$.
Name |
---|