题目描述
Consider the following game:
There are two players, First and Second, sitting in front of a pile of $n$ stones. First always plays first.
There is a set, $\mbox{S}$, of $m$ distinct integers defined as $S=\{s_0,s_1,\ldots,s_{m-1}\}$.
The players move in alternating turns. During each turn, a player chooses some $s_i\in S$ and splits one of the piles into exactly $s_i$ smaller piles of equal size. If no $s_i$ exists that will split one of the available piles into exactly $s_i$ equal smaller piles, the player loses.
Both players always play optimally.
Given $n$, $m$, and the contents of $\mbox{S}$, find and print the winner of the game. If First wins, print First; otherwise, print Second.
Input Format
The first line contains two space-separated integers describing the respective values of $n$ (the size of the initial pile) and $m$ (the size of the set).
The second line contains $m$ distinct space-separated integers describing the respective values of $s_0,s_1,\ldots,s_{m-1}$.
Constraints
$1\leq n\leq10^{18}$
$1\leq m\leq10$
$2\leq s_i\leq10^{18}$
Output Format
Print First if the First player wins the game; otherwise, print Second.
Sample Input 0
15 3
5 2 3
Sample Output 0
Second
Explanation 0
The initial pile has $n=15$ stones, and $S=\{5,2,3\}$. During First's initial turn, they have two options:
Split the initial pile into $5$ equal piles, which forces them to lose after the following sequence of turns:
Split the initial pile into $3$ equal piles, which forces them to lose after the following sequence of turns:
Because First never has any possible move that puts them on the path to winning, we print Second as our answer.
输入格式
见题面
输出格式
见题面