Yet Another Stone Game

There are $N$ piles of stones. The $i$-th pile initially contains $A_i$ stones. An integer $K$ is also given.

The first and second players alternate turns, starting with the first player. On each turn, the player performs the following move.

• Choose between $1$ and $K$ distinct nonempty piles.
• Remove one stone from each chosen pile.

A player who cannot make a move loses. Determine the winner when both players play optimally.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, print First if the first player wins, or Second if the second player wins.

• $1\leq T\leq100\,000$.
• $3\leq N\leq300\,000$.
• $N-2$.