#K5671. Chest Game: Determine the Winner

    ID: 30259 Type: Default 1000ms 256MiB

Chest Game: Determine the Winner

Chest Game: Determine the Winner

Two players are playing a coin collection game involving M chests. Each chest contains some coins. In each move, a player may collect coins from one or more chests with the following restrictions:

  • The maximum number of coins that can be taken in a single move is given by K.
  • If the total number of coins in all chests is less than or equal to K, the first player wins immediately.
  • If any individual chest contains more than K coins, then the move is illegal for the first player and the second player wins.
  • Otherwise, the game proceeds in turns. The winner is determined by the parity of the number of full moves possible. In other words, if \(\left\lfloor \frac{\text{total coins}}{K} \right\rfloor\) is odd, the first player wins; if it is even, the second player wins.

Your task is to implement a program that, given the parameters of the game, determines the winner as either "First" or "Second".

inputFormat

The input is read from standard input (stdin) and is formatted as follows:

M K
c1 c2 ... cM

Where:

  • M is the number of chests.
  • K is the maximum number of coins that can be collected in one move.
  • ci represents the number of coins in the i-th chest.

outputFormat

Output a single line to standard output (stdout) containing either "First" if the first player wins or "Second" if the second player wins.

## sample
3 5
1 2 3
First

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