#abc297g. [abc297_g]Constrained Nim 2

[abc297_g]Constrained Nim 2

Problem Statement

There are NN piles of stones. Initially, the ii-th pile contains AiA_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 LL and RR 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

  • 1leqNleq2times1051\\leq N \\leq 2\\times 10^5
  • 1leqLleqRleq1091\\leq L \\leq R \\leq 10^9
  • 1leqAileq1091\\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:

NN LL RR A1A_1 A2A_2 ldots\\ldots ANA_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