Points: $900$ points

问题陈述

玩家Alice和Bob使用长度为$N$的序列$L$和$R$进行游戏，规则如下：

• 游戏由$N$个回合组成。
• 如果$i$是奇数，第$i$个回合由Alice进行；如果$i$是偶数，第$i$个回合由Bob进行。
• 游戏开始时，有一个包含一些石头的堆。
• 对于$i=1,2,\dots,N$，按照这个顺序，他们执行以下操作（称为第$i$个回合）：
  • 进行第$i$个回合的玩家从堆中取走$L_i$到$R_i$（包括$L_i$和$R_i$）之间的整数个石头。
  • 如果玩家不能取走满足上述条件的石头，他们就输了，另一个玩家赢了。
• 如果到第$N$个回合结束时，没有玩家输掉游戏，游戏以平局结束。

游戏开始前，两位玩家都会知道序列$L$和$R$以及游戏开始时堆中的石头数量。

可以证明，游戏恰好有以下三种结果之一：

• Alice ... Alice有一个获胜策略。
• Bob ... Bob有一个获胜策略。
• Draw ... 没有玩家有获胜策略。

回答关于这个游戏的$Q$个问题。第$i$个问题如下：

• 假设游戏开始时堆中包含$C_i$个石头。报告游戏的结果：Alice、Bob或Draw。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

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 $i$ is played by Bob.
• Initially, there is a pile with some number of stones.
• For $i=1,2,\dots,N$ in this order, they perform the following operation (called turn $i$):
  • The player who plays turn $i$ takes an integer number of stones between $L_i$ and $R_i$, inclusive, from the pile.
  • If the player cannot take stones satisfying the above, they lose, and the other player wins.
• If neither player has lost by the end of turn $N$, the game ends in a draw.

Before 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.

It can be proved that the game has exactly one of the following three consequences:

• Alice ... Alice has a winning strategy.
• Bob ... Bob has a winning strategy.
• Draw ... Neither player has a winning strategy.

Answer $Q$ queries about this game. The $i$-th query is as follows:

• Assume that the pile contains $C_i$ stones at the start of the game. Report the consequence of the game: Alice, Bob, or Draw.

Constraints

• $N$, $L_i$, $R_i$, $Q$, and $C_i$ are integers.
• $1 \le N \le 3 \times 10^5$
• $1 \le L_i \le R_i \le 10^9$
• $1 \le Q \le 3 \times 10^5$
• $1 \le C_i \le \sum_{i=1}^{N} R_i$

Input

The input is given from Standard Input in the following format:

$N$

$L_1$ $R_1$

$L_2$ $R_2$

$\vdots$

$L_N$ $R_N$

$Q$

$C_1$

$C_2$

$\vdots$

$C_Q$

Output

Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query.

Sample Input 1

4
1 3
1 2
3 4
1 2
11
1
2
3
4
5
6
7
8
9
10
11

Sample Output 1

Alice
Alice
Alice
Bob
Bob
Alice
Alice
Alice
Draw
Draw
Draw

This input contains $11$ queries.

• 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.
• When $4 \le C_i \le 5$, Bob has a winning strategy.
• When $6 \le C_i \le 8$, Alice has a winning strategy.
• When $C_i \ge 9$, neither player has a winning strategy.
  • For example, if $C_i=9$, the game could proceed as follows:
    • On turn $1$, Alice takes $3$ stones. $6$ stones remain.
    • On turn $2$, Bob takes $1$ stone. $5$ stones remain.
    • On turn $3$, Alice takes $4$ stones. $1$ stone remains.
    • On turn $4$, Bob takes $1$ stone. No stones remain.
    • Since neither player has lost by the end of turn $4$, the game ends in a draw.
  • 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).