E. Carrots for Rabbitstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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.OutputOutput one integer: the minimum sum of time taken for rabbits to eat carrots.ExamplesInput
3 6
5 3 1
Output
15
Input
1 4
19
Output
91
NoteFor 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=15For 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.
3 6
5 3 1

15 
['binary search', 'data structures', 'greedy', 'math', 'sortings', '*2200']