题目描述
$\documentclass{article}$
$\usepackage{graphicx}$ % Required for inserting images
$\title{test}$
$\author{z1284537530 }$
$\date{March 2023}$
$\begin{document}$
$\maketitle$
After their success in coming up with Fun Game, Kyle and Mike invented another game having the following rules:
The game starts with an $n$-element sequence, $*2^1*2^2*2^3*\ldots*2^n$, and is played by two players, $\mathbf{P_1}$ and $P_2$.
The players move in alternating turns, with $\mathbf{P_1}$ always moving first. During each move, the current player chooses one of the asterisks ($\lt\:k$) in the above sequence and changes it to either a + (plus) or a - (minus) sign.
The game ends when there are no more asterisks ($\lt\:k$) in the expression. If the evaluated value of the sequence is divisible by $17$, then $P_2$ wins; otherwise, $\mathbf{P_1}$ wins.
Given the value of $n$, can you determine the outcome of the game? Print $\textbf{First}$ if $\mathbf{P_1}$ will win, or $\textbf{Second}$ if $P_2$ will win. Assume both players always move optimally.
Input Format
The first line of input contains a single integer $\mathbf{T}$, denoting the number of test cases.
Each line $\boldsymbol{i}$ of the $\mathbf{T}$ subsequent lines contains an integer, $n$, denoting the maximum exponent in the game's initial sequence.
Constraints
$1\leq T\leq10^6$
$1\leq n\leq10^{6}$
Output Format
For each test case, print either of the following predicted outcomes of the game on a new line:
Print $\textbf{First}$ if $\mathbf{P_1}$ will win.
Print $\textbf{Second}$ if $P_2$ will win.
Sample Input
1
2
Sample Output
First
Explanation
In this case, it doesn't matter in which order the asterisks are chosen and altered. There are $\begin{array}{c}4\end{array}$ different courses of action and, in each one, the final value is not divisible by $17$ (so $P_2$ always loses and we print $\textbf{First}$ on a new line).
Possible options:
$+2^1+2^2=6$
$+2^1-2^2=-2$
$-2^1+2^2=2$
$-2^1-2^2=-6$
$\section{Introduction}$
$\end{document}$
输入格式
见题面
输出格式
见题面