CF1428E.Carrots for Rabbits

There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought $n$ carrots with lengths $a_1, a_2, a_3, \ldots, a_n$. However, rabbits are very fertile and multiply very quickly. Zookeeper now has $k$ rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut the carrots into $k$ pieces. For some reason, all resulting carrot lengths must be positive integers.

Big carrots are very difficult for rabbits to handle and eat, so the time needed to eat a carrot of size $x$ is $x^2$.

Help Zookeeper split his carrots while minimizing the sum of time taken for rabbits to eat the carrots.

新加坡动物园里有一些兔子。为了喂养它们，饲养员购买了 $n$ 根胡萝卜，长度分别为 $a_1, a_2, a_3, \ldots, a_n$。然而，兔子繁殖能力极强，数量增长很快。如今饲养员有 $k$ 只兔子，但胡萝卜数量不足，无法喂饱所有兔子。为解决这一问题，饲养员决定将胡萝卜切成总共 $k$ 段。出于某种原因，所有切分后胡萝卜的长度必须为正整数。

大块胡萝卜对兔子而言很难处理和进食，因此兔子吃掉一根长度为 $x$ 的胡萝卜所需时间为 $x^2$。

请帮助饲养员切分胡萝卜，使得所有兔子吃完胡萝卜所需的总时间最小。

The first line contains two integers $n$ and $k$ $(1 \leq n \leq k \leq 10^5)$: the initial number of carrots and the number of rabbits.

The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \leq a_i \leq 10^6)$: lengths of carrots.

It is guaranteed that the sum of $a_i$ is at least $k$.

第一行包含两个整数 $n$ 和 $k$ $(1 \leq n \leq k \leq 10^5)$：初始胡萝卜的数量和兔子的数量。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$ $(1 \leq a_i \leq 10^6)$：胡萝卜的长度。

保证所有 $a_i$ 的总和至少为 $k$。

Output one integer: the minimum sum of time taken for rabbits to eat carrots.

输出一个整数：兔子吃胡萝卜所需时间的最小总和。

For the first test, the optimal sizes of carrots are ${1,1,1,2,2,2}$. The time taken is $1^2+1^2+1^2+2^2+2^2+2^2=15$

For the second test, the optimal sizes of carrots are ${4,5,5,5}$. The time taken is $4^2+5^2+5^2+5^2=91$.

对于第一个测试用例，胡萝卜的最优尺寸为 ${1,1,1,2,2,2}$。所用时间为 $1^2+1^2+1^2+2^2+2^2+2^2=15$。

对于第二个测试用例，胡萝卜的最优尺寸为 ${4,5,5,5}$。所用时间为 $4^2+5^2+5^2+5^2=91$。