B. Road to Arabella

Codeforces

IDCF10226B

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Ayoub and Kilani felt board while they are going to ArabellaCPC in (Amman-Irbid) road, so Kilani invented a new game to play with Ayoub. The game is described by the following rules : Ayoub picks a random integer $n$ $(1 <= n <= 10^9)$ , and Kilani picks a random integer $k$ $(1 <= k <= n)$, then they will start playing. In each turn a player can choose any number $x$ $(1 <= x <= m a x (1, m -k))$ (which $m$ is the current value of $n$) and subtract it from $n$. if $n$ equals zero then the player can't make a move. The player who can't make a move is considered to lose the game. If Kilani starts, and each player played optimally, who would be the winner? First line of input contains integer $T$ $(1 <= T <= 10^4)$ the number of test cases. Each one of next $T$ lines contains two integers $n$ and $k$, $(1 <= k <= n <= 10^9)$. print "Kilani" if he wins, and print "Ayoub" otherwise. (the output is case sensitive) ## Input First line of input contains integer $T$ $(1 <= T <= 10^4)$ the number of test cases.Each one of next $T$ lines contains two integers $n$ and $k$, $(1 <= k <= n <= 10^9)$. ## Output print "Kilani" if he wins, and print "Ayoub" otherwise. (the output is case sensitive) [samples]

**Definitions** Let $ n \in \mathbb{P} $ be a given prime number, where $ 2 \leq n \leq 10^7 $. Let $ \mathbb{P} $ denote the set of prime numbers. **Objective** Find $ a, b \in \mathbb{P} $ such that $ a + b = n $. If no such pair exists, output $-1$.

API Response (JSON)

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