B"Uh oh! Applications to tech companies are due soon, and you've been procrastinating by doing contests instead! (Let's pretend for now that it is actually possible to get a job in these uncertain times.) You have completed many programming projects. In fact, there are exactly n types of programming projects, and you have completed a_i projects of type i . Your r xc3 xa9sum xc3 xa9 has limited space, but you want to carefully choose them in such a way that maximizes your chances of getting hired. You want to include several projects of the same type to emphasize your expertise, but you also don't want to include so many that the low-quality projects start slipping in. Specifically, you determine the following quantity to be a good indicator of your chances of getting hired: f(b_1, ldots,b_n)= sum limits_{i=1}^n b_i(a_i-b_i^2). Here, b_i denotes the number of projects of type i you include in your r xc3 xa9sum xc3 xa9. Of course, you cannot include more projects than you have completed, so you require 0 <= b_i <= a_i for all i . Your r xc3 xa9sum xc3 xa9 only has enough room for k projects, and you will absolutely not be hired if your r xc3 xa9sum xc3 xa9 has empty space, so you require sum limits_{i=1}^n b_i=k . Find values for b_1, ldots, b_n that maximize the value of f(b_1, ldots,b_n) while satisfying the above two constraints. The first line contains two integers n and k ( 1 <= n <= 10^5 , 1 <= k <= sum limits_{i=1}^n a_i ) -- the number of types of programming projects and the r xc3 xa9sum xc3 xa9 size, respectively. The next line contains n integers a_1, ldots,a_n ( 1 <= a_i <= 10^9 ) -- a_i is equal to the number of completed projects of type i . In a single line, output n integers b_1, ldots, b_n that achieve the maximum value of f(b_1, ldots,b_n) , while satisfying the requirements 0 <= b_i <= a_i and sum limits_{i=1}^n b_i=k . If there are multiple "...