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Coin Tower Game

Time limit1sMemory limit512 MB

Summary
Two players take coins from two towers, and the one who takes the last coin gains or loses K coins. Find whether Yeongdo should move first or second to win.
Level

Medium7 of 10

Topics
Game theory, Dynamic programming
Solved
No attempts yet

Problem

The coin tower game is played by two players, each with two towers of AA and BB coins. The players take turns. On each turn, a player picks one non-empty tower and takes at least one coin from it. When no coins are left to take, the game ends and the player who took more coins wins. If both players took the same number of coins, the second player wins.

Mingyu wanted to make this simple game more interesting. So he chose an integer KK, so that the outcome stays unknown until the game ends, and added this rule for the player who takes the last coin.

  • If KK is a non-negative integer, that player gains KK extra coins.
  • If KK is negative, that player loses ∣K∣\left\vert K \right\vert coins. If the player has fewer than ∣K∣\left\vert K \right\vert coins, that player loses the game.

Mingyu plays this improved game with Yeongdo. Yeongdo spotted the winning strategy as soon as he saw the game, and quickly took the choice of going first or second. Assuming both players play optimally, should Yeongdo choose to go first or second in order to win?

Input

The first line contains AA, BB, and KK, separated by spaces.

Output

If Yeongdo should go first, print "First". If he should go second, print "Second".

Constraints

  • 0≤A,B≤1 0000 \le A, B \le 1\,000
  • A+B>0A+B > 0
  • ∣K∣≤2 000\left\vert K \right\vert \le 2\,000
  • All numbers in the input are integers.

Examples2

  1. Example 1

    Input
    10 7 4
    
    Expected output
    First
    
  2. Example 2

    Input
    4 4 -2
    
    Expected output
    Second