Carrots for Rabbits

1000ms

262144K

Description:

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.

Input:

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:

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

Sample Input:

3 6
5 3 1

Sample Output:

Sample Input:

1 4
19

Sample Output:

Note:

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 $$$4^2+5^2+5^2+5^2=91$$$.

Informação

Provedor Codeforces

Código CF1428E