#abc297g. [abc297_g]Constrained Nim 2
[abc297_g]Constrained Nim 2
Problem Statement
There are piles of stones. Initially, the -th pile contains 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 and 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
- All values in the input are integers.
Input
The input is given from Standard Input in the following format:
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