CF830C.Bamboo Partition

Vladimir wants to modernize partitions in his office. To make the office more comfortable he decided to remove a partition and plant several bamboos in a row. He thinks it would be nice if there are $n$ bamboos in a row, and the $i$-th from the left is $a_i$ meters high.

Vladimir has just planted $n$ bamboos in a row, each of which has height $0$ meters right now, but they grow $1$ meter each day. In order to make the partition nice Vladimir can cut each bamboo once at any height (no greater that the height of the bamboo), and then the bamboo will stop growing.

Vladimir wants to check the bamboos each $d$ days (i.e. $d$ days after he planted, then after $2d$ days and so on), and cut the bamboos that reached the required height. Vladimir wants the total length of bamboo parts he will cut off to be no greater than $k$ meters.

What is the maximum value $d$ he can choose so that he can achieve what he wants without cutting off more than $k$ meters of bamboo?

弗拉基米尔希望改造办公室的隔断。为了让办公室更加舒适，他决定拆除一道隔断，并在一行中种植若干竹子。他觉得如果一行中有 $n$ 根竹子，且从左往右第 $i$ 根竹子的高度恰好为 $a_i$ 米，那就非常美观。

弗拉基米尔刚刚在一排种下了 $n$ 根竹子，每根竹子当前高度均为 $0$ 米，但它们每天均长高 $1$ 米。为了使隔断达到理想效果，弗拉基米尔可以对每根竹子至多修剪一次（剪裁位置不能高于该竹子当前高度），此后该竹子将停止生长。

弗拉基米尔计划每隔 $d$ 天检查一次竹子（即在种下后第 $d$ 天、第 $2d$ 天、……时进行检查），并对已达到目标高度的竹子进行修剪。他希望所有被剪下的竹子部分的总长度不超过 $k$ 米。

请问：满足上述要求的前提下，弗拉基米尔所能选择的最大 $d$ 值是多少？

The first line contains two integers $n$ and $k$ ($1 \le n \le 100$, $1 \le k \le 10^{11}$) — the number of bamboos and the maximum total length of cut parts, in meters.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$) — the required heights of bamboos, in meters.

第一行包含两个整数 $n$ 和 $k$（$1 \le n \le 100$，$1 \le k \le 10^{11}$）—— 分别表示竹子的数量以及被截去部分的总长度上限（单位：米）。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$）—— 表示每根竹子所需达到的高度（单位：米）。

Print a single integer — the maximum value of $d$ such that Vladimir can reach his goal.

输出一个整数——即 Vladimir 能够达成目标的最大 $d$ 值。

In the first example Vladimir can check bamboos each $3$ days. Then he will cut the first and the second bamboos after $3$ days, and the third bamboo after $6$ days. The total length of cut parts is $2+0+1=3$ meters.

在第一个例子中，弗拉基米尔可以每 $3$ 天检查一次竹子。这样，他将在 $3$ 天后砍掉第一根和第二根竹子，$6$ 天后砍掉第三根竹子。被砍下的部分总长度为 $2+0+1=3$ 米。