310601: CF1858A. Buttons
Description
Anna and Katie ended up in a secret laboratory.
There are $a+b+c$ buttons in the laboratory. It turned out that $a$ buttons can only be pressed by Anna, $b$ buttons can only be pressed by Katie, and $c$ buttons can be pressed by either of them. Anna and Katie decided to play a game, taking turns pressing these buttons. Anna makes the first turn. Each button can be pressed at most once, so at some point, one of the girls will not be able to make her turn.
The girl who cannot press a button loses. Determine who will win if both girls play optimally.
InputThe first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
Each test case consists of three integers $a$, $b$, and $c$ ($1 \le a, b, c \le 10^9$) — the number of buttons that can only be pressed by Anna, the number of buttons that can only be pressed by Katie, and the number of buttons that can be pressed by either of them, respectively.
OutputFor each test case, output First if Anna wins, or Second if Katie wins.
ExampleInput5 1 1 1 9 3 3 1 2 3 6 6 9 2 2 8Output
First First Second First SecondNote
For the simplicity of the explanation, we will numerate the buttons by the numbers from $1$ to $a+b+c$: the first $a$ buttons can only be pressed by Anna, the next $b$ buttons can only be pressed by Katie, and the last $c$ buttons can be pressed by either of them.
In the first test case, Anna can press the $3$-rd button on the first turn. Then Katie will press the $2$-nd button (since it is the only possible turn for her). Then Anna will press the $1$-st button. Katie won't have a button to press, so Anna will win.
In the second test case, Anna can press the first nine buttons in some order on her turns. No matter what buttons Katie will press, all the buttons from the $10$-th to the $15$-th will be pressed after $12$ turns. On the $13$-th turn, Anna will press one of the first nine buttons and Katie will not have a button to press on her turn. Thus, Anna will win.
In the third test case, the game can proceed as follows:
- On the $1$-st turn Anna presses the $5$-th button.
- On the $2$-st turn Katie presses the $4$-th button.
- On the $3$-st turn Anna presses the $6$-th button.
- On the $4$-st turn Katie presses the $3$-th button.
- On the $5$-st turn Anna presses the $1$-th button.
- On the $6$-st turn Katie presses the $2$-th button.
- Anna cannot make the turn, so Katie wins.
It can be shown that Katie can win no matter what moves Anna takes.
Output
Anna和Katie在一个秘密实验室里，面前有a+b+c个按钮。其中a个按钮只能由Anna按，b个按钮只能由Katie按，c个按钮两人都可以按。她们轮流按下这些按钮，Anna先开始。每个按钮最多被按一次，直到某个女孩无法按下一个按钮为止。无法按下按钮的女孩将输掉游戏。如果两人都采取最佳策略，确定谁会赢。
输入数据格式：
第一行包含一个整数t（1≤t≤10^4），表示测试用例的数量。
每个测试用例包含三个整数a、b和c（1≤a,b,c≤10^9），分别表示只能由Anna按的按钮数量、只能由Katie按的按钮数量以及两人都可以按的按钮数量。
输出数据格式：
对于每个测试用例，如果Anna赢，输出"First"，如果Katie赢，输出"Second"。题目大意： Anna和Katie在一个秘密实验室里，面前有a+b+c个按钮。其中a个按钮只能由Anna按，b个按钮只能由Katie按，c个按钮两人都可以按。她们轮流按下这些按钮，Anna先开始。每个按钮最多被按一次，直到某个女孩无法按下一个按钮为止。无法按下按钮的女孩将输掉游戏。如果两人都采取最佳策略，确定谁会赢。 输入数据格式： 第一行包含一个整数t（1≤t≤10^4），表示测试用例的数量。 每个测试用例包含三个整数a、b和c（1≤a,b,c≤10^9），分别表示只能由Anna按的按钮数量、只能由Katie按的按钮数量以及两人都可以按的按钮数量。 输出数据格式： 对于每个测试用例，如果Anna赢，输出"First"，如果Katie赢，输出"Second"。