P9586 "MXOI Round 2" Game

Xiao C and Xiao D are playing a fast-growing game. This game has a total of $3$ types of hand cards: Kill, Dodge, Slash. Their uses are as follows: - Kill: use it on the opponent; the opponent must use a **Dodge**, otherwise the opponent loses the game; **or** respond to the opponent’s **Slash**. - Dodge: respond to the opponent’s **Kill**. - Slash: use it on the opponent; the opponent must use a **Kill**, otherwise the opponent loses the game. After a player uses a card, they must discard the card they used. Starting from Xiao C, each turn belongs to Xiao C and Xiao D alternately. During a player’s turn, that player may play **any number** of **Kill** and **Slash**, and the opponent must make the corresponding responses. Of course, the player may also choose not to play any card and directly enter the opponent’s turn. Now, Xiao C has $c_1$ Kill cards, $c_2$ Dodge cards, and $c_3$ Slash cards; Xiao D has $d_1$ Kill cards, $d_2$ Dodge cards, and $d_3$ Slash cards. **Both sides know each other’s hands**. You need to determine what the result of the game will be when both sides use optimal strategies.

**This problem contains multiple test cases.** The first line contains an integer $T$, representing the number of test cases. Then for each test case, one line contains six integers $c_1,c_2,c_3,d_1,d_2,d_3$.

For each test case, output one line: - If, under optimal play from both sides, Xiao C can win, output `C`. - If, under optimal play from both sides, Xiao D can win, output `D`. - If, under optimal play from both sides, the game ends in a draw, meaning neither side can win, output `E`.

#### Sample Explanation #1 For the first set of data, Xiao C can play a Slash first, and after Xiao D responds with a Kill, play another Slash. At this time, Xiao D has used up all Kill cards and cannot respond, so Xiao D loses the game. #### Sample #2 See `game/game2.in` and `game/game2.ans` in the additional files. #### Constraints For $100\%$ of the testdata, $1 \le T \le 10^5$, $0 \le c_1,c_2,c_3,d_1,d_2,d_3 \le 10^9$. |Test Point ID|Special Property| |:---:|---| |$1\sim3$|Guarantee $c_3=d_3=0$.| |$4\sim6$|Guarantee $c_1=d_2$ and $c_2=d_1$.| |$7\sim10$|None.| Translated by ChatGPT 5