{"problem":{"name":"Subset Sum Game","description":{"content":"There are $N$ integers written on a blackboard. The $i$\\-th integer is $A_i$. Here, $N$ is even. Additionally, integers $L$ and $R$ are given. Alice and Bob will play a game. They alternately take tur","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc056_d"},"statements":[{"statement_type":"Markdown","content":"There are $N$ integers written on a blackboard. The $i$\\-th integer is $A_i$. Here, $N$ is even. Additionally, integers $L$ and $R$ are given.\nAlice and Bob will play a game. They alternately take turns, with Alice going first. In each turn, the player chooses a number written on the blackboard and erases it.\nThe game will end in $N$ turns. Then, let $s$ be the sum of the integers erased by Alice. If $L \\leq s \\leq R$, Alice wins; otherwise, Bob wins. Find which player will win when both players play optimally.\n\n## Constraints\n\n*   $2 \\leq N \\leq 5000$\n*   $N$ is even.\n*   $1 \\leq A_i \\leq 10^9$\n*   $0 \\leq L \\leq R \\leq \\sum_{1 \\leq i \\leq N} A_i$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $L$ $R$\n$A_1$ $A_2$ $\\cdots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc056_d","tags":[],"sample_group":[["4 5 6\n3 1 4 5","Alice\n\nIn this game, Alice will always win. Below is a possible progression of the game.\n\n*   Alice erases $1$.\n*   Bob erases $4$.\n*   Alice erases $5$.\n*   Bob erases $3$.\n\nHere, the sum of the integers erased by Alice is $6$. Since $L \\leq 6 \\leq R$, Alice wins."],["2 2 3\n4 1","Bob"],["30 655 688\n42 95 9 13 91 27 99 56 64 15 3 11 5 16 85 3 62 100 64 79 1 70 8 69 70 28 78 4 33 12","Bob"],["30 792 826\n81 60 86 57 5 20 26 13 39 64 89 58 43 98 50 79 58 21 27 68 46 47 45 85 88 5 82 90 74 57","Alice"]],"created_at":"2026-03-03 11:01:14"}}