102976: [Atcoder]ABC297 G - Constrained Nim 2

Problem Statement

There are $N$ piles of stones. Initially, the $i$-th pile contains $A_i$ stones. With these piles, Taro the First and Jiro the Second play a game against each other.

Taro the First and Jiro the Second make the following move alternately, with Taro the First going first:

• Choose a pile of stones, and remove between $L$ and $R$ stones (inclusive) from it.

A player who is unable to make a move loses, and the other player wins. Who wins if they optimally play to win?

Constraints

• $1\leq N \leq 2\times 10^5$
• $1\leq L \leq R \leq 10^9$
• $1\leq A_i \leq 10^9$
• All values in the input are integers.

Input

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

$N$ $L$ $R$ 
$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print First if Taro the First wins; print Second if Jiro the Second wins.

Sample Input 1

3 1 2
2 3 3

Sample Output 1

First

Taro the First can always win by removing two stones from the first pile in his first move.

Sample Input 2

5 1 1
3 1 4 1 5

Sample Output 2

Second

Sample Input 3

7 3 14
10 20 30 40 50 60 70

Sample Output 3

First

问题描述

有N堆石头。最初，第i堆包含Ai个石头。用这些石头，大郎和次郎轮流进行游戏。

大郎和次郎轮流进行以下操作，大郎先进行：

• 选择一堆石头，从中移除L到R（含）个石头。

无法进行操作的玩家输掉游戏，另一名玩家获胜。如果他们优化操作以求获胜，谁会赢呢？

约束

• $1\leq N \leq 2\times 10^5$
• $1\leq L \leq R \leq 10^9$
• $1\leq A_i \leq 10^9$
• 输入中的所有值都是整数。

输入

输入以标准输入的以下格式给出：

$N$ $L$ $R$ 
$A_1$ $A_2$ $\ldots$ $A_N$

输出

如果大郎获胜，则打印First；如果次郎获胜，则打印Second。

样例输入1

3 1 2
2 3 3

样例输出1

First

大郎总可以在他的第一次操作中从第一堆中移除两个石头来获胜。

样例输入2

5 1 1
3 1 4 1 5

样例输出2

Second

样例输入3

7 3 14
10 20 30 40 50 60 70

样例输出3

First