{"problem":{"name":"B. Road to Arabella","description":{"content":"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 ","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10226B"},"statements":[{"statement_type":"Markdown","content":"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.\n\nThe game is described by the following rules :\n\nAyoub 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.\n\nIf Kilani starts, and each player played optimally, who would be the winner?\n\nFirst line of input contains integer $T$ $(1 <= T <= 10^4)$ the number of test cases.\n\nEach one of next $T$ lines contains two integers $n$ and $k$, $(1 <= k <= n <= 10^9)$.\n\nprint \"Kilani\" if he wins, and print \"Ayoub\" otherwise. (the output is case sensitive) \n\n## Input\n\nFirst 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 $k$, $(1 <= k <= n <= 10^9)$.\n\n## Output\n\nprint \"Kilani\" if he wins, and print \"Ayoub\" otherwise. (the output is case sensitive) \n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ n \\in \\mathbb{P} $ be a given prime number, where $ 2 \\leq n \\leq 10^7 $.  \nLet $ \\mathbb{P} $ denote the set of prime numbers.\n\n**Objective**  \nFind $ a, b \\in \\mathbb{P} $ such that $ a + b = n $.  \nIf no such pair exists, output $-1$.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10226B","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}