{"problem":{"name":"Final Stage","description":{"content":"Players Alice and Bob play a game using sequences $L$ and $R$ of length $N$, as follows. *   The game consists of $N$ turns. *   If $i$ is odd, turn $i$ is played by Alice; if $i$ is even, turn $i$ i","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":4000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc174_f"},"statements":[{"statement_type":"Markdown","content":"Players Alice and Bob play a game using sequences $L$ and $R$ of length $N$, as follows.\n\n*   The game consists of $N$ turns.\n*   If $i$ is odd, turn $i$ is played by Alice; if $i$ is even, turn $i$ is played by Bob.\n*   Initially, there is a pile with some number of stones.\n*   For $i=1,2,\\dots,N$ in this order, they perform the following operation (called turn $i$):\n    *   The player who plays turn $i$ takes an integer number of stones between $L_i$ and $R_i$, inclusive, from the pile.\n    *   If the player cannot take stones satisfying the above, they lose, and the other player wins.\n*   If neither player has lost by the end of turn $N$, the game ends in a draw.\n\nBefore the game starts, both players are informed of the sequences $L$ and $R$ and the number of stones in the pile at the start of the game.\nIt can be proved that the game has exactly one of the following three **consequences**:\n\n*   `Alice` ... Alice has a winning strategy.\n*   `Bob` ... Bob has a winning strategy.\n*   `Draw` ... Neither player has a winning strategy.\n\nAnswer $Q$ queries about this game. The $i$\\-th query is as follows:\n\n*   Assume that the pile contains $C_i$ stones at the start of the game. Report the consequence of the game: `Alice`, `Bob`, or `Draw`.\n\n## Constraints\n\n*   $N$, $L_i$, $R_i$, $Q$, and $C_i$ are integers.\n*   $1 \\le N \\le 3 \\times 10^5$\n*   $1 \\le L_i \\le R_i \\le 10^9$\n*   $1 \\le Q \\le 3 \\times 10^5$\n*   $1 \\le C_i \\le \\sum_{i=1}^{N} R_i$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$L_1$ $R_1$\n$L_2$ $R_2$\n$\\vdots$\n$L_N$ $R_N$\n$Q$\n$C_1$\n$C_2$\n$\\vdots$\n$C_Q$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc174_f","tags":[],"sample_group":[["4\n1 3\n1 2\n3 4\n1 2\n11\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11","Alice\nAlice\nAlice\nBob\nBob\nAlice\nAlice\nAlice\nDraw\nDraw\nDraw\n\nThis input contains $11$ queries.\n\n*   When $C_i \\le 3$, Alice can take all $C_i$ stones on turn $1$, leaving no stones in the pile, so Alice has a winning strategy.\n*   When $4 \\le C_i \\le 5$, Bob has a winning strategy.\n*   When $6 \\le C_i \\le 8$, Alice has a winning strategy.\n*   When $C_i \\ge 9$, neither player has a winning strategy.\n    *   For example, if $C_i=9$, the game could proceed as follows:\n        *   On turn $1$, Alice takes $3$ stones. $6$ stones remain.\n        *   On turn $2$, Bob takes $1$ stone. $5$ stones remain.\n        *   On turn $3$, Alice takes $4$ stones. $1$ stone remains.\n        *   On turn $4$, Bob takes $1$ stone. No stones remain.\n        *   Since neither player has lost by the end of turn $4$, the game ends in a draw.\n    *   Various other progressions are possible, but it can be shown that when $C_i=9$, neither player has a winning strategy (if both players play optimally, the game will end in a draw)."]],"created_at":"2026-03-03 11:01:14"}}