P24498 [AtCoder] Constrained Nim 2
提高-
题目描述

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?

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.

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.

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

输入格式

见题面 Input 部分

输出格式

见题面 Output 部分

样例输入
3 1 2 2 3 3
样例输出
First