Carrots for Rabbits

新加坡动物园里有一些 `兔`。为了喂养他们，管理员买了 $n$ 根胡萝卜 $a_1,a_2,a_3, \dots, a_n$。然而，`兔` 很肥且繁殖很快。管理员现在有 $k$ 只 `兔` 却没有足够的胡萝卜去喂它们。管理员需要把 $n$ 根胡萝卜切成 $k$ 根胡萝卜以喂养 $k$ 只 `兔`。出于某种原因，所有胡萝卜（包括切出来的胡萝卜）的长度必须为正整数。 `兔` 很难拿稳大萝卜，也很难咽下大萝卜，所以吃掉一个长度为 $x$ 的萝卜所需要的时间是 $x^2$。 现在请你帮助管理员切这些萝卜，以最小化 `兔` 吃萝卜的总时间。 --- 数据范围：$1\leq n \leq k \leq 10^5,1 \leq a_i \leq 10^6$

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.

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 $ .

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

3 6
5 3 1

15

1 4
19

91

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 $ .