Ggeureuda Gimgganom

Jeongrae runs a gimbap factory that makes gimbap to supply to the gimbap restaurant "Ggeureuda Gimgganom". Jeongrae calls the two ends of a gimbap roll its "tails", and a gimbap roll with its tails cut off a "trimmed gimbap".

The factory processes $N$ gimbap rolls: it cuts off the tails and turns the trimmed gimbap into gimbap pieces. When cutting off the tails, it cuts a uniform $K$ cm from both ends. If a roll is shorter than $2K$ cm, so that only one end can be cut, only one tail is cut off. If a roll is $K$ cm or shorter, it is discarded.

Every trimmed gimbap is then cut into pieces of a constant length $P$, giving $P$ cm gimbap pieces. $P$ must be a positive integer. Jeongrae wants to make at least $M$ gimbap pieces cut to the constant length $P$ cm. Find the value $P$ should be set to when $P$ is to be as long as possible.

The first line gives the number of gimbap rolls to trim, $N$, the tail length $K$, and the minimum number of gimbap pieces, $M$. ($1 \le N \le 10^6$, $1 \le K, M \le 10^9$, $N$, $K$, $M$ are integers)

Starting from the second line, the lengths $L$ of $N$ gimbap rolls are given. ($1 \le L \le 10^9$, $L$ is an integer)

Print $P$, the maximum possible length of a gimbap piece. If no such $P$ exists, print -1.