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G - Constrained Nim 2

Score : $600$ points

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.

3 1 2
2 3 3

First

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

5 1 1
3 1 4 1 5

Second

7 3 14
10 20 30 40 50 60 70

First