- Time limit: 1.00 s
- Memory limit: 512 MB
There are two players who move alternately. On each move, a player chooses a stair $k$ where $k \neq 1$ and it has at least one ball. Then, the player moves any number of balls from stair $k$ to stair $k-1$. The winner is the player who moves last.
Your task is to find out who wins the game when both players play optimally.
The first input line has an integer $t$: the number of tests. After this, $t$ test cases are described:
The first line contains an integer $n$: the number of stairs.
The next line has $n$ integers $p_1,p_2,\ldots,p_n$: the initial number of balls on each stair.
For each test, print "first" if the first player wins the game and "second" if the second player wins the game.
- $1 \le t \le 2 \cdot 10^5$
- $1 \le n \le 2 \cdot 10^5$
- $0 \le p_i \le 10^9$
- the sum of all $n$ is at most $2 \cdot 10^5$
0 2 1
1 1 1 1