P2112 Wild Goose Mail

Xiao Ming wrote a love letter to Xiao Hong. He wants to make it more perfect, so he needs to typeset it.

He wrote $N$ words in total. For aesthetics, you must split the $N$ words into $K$ lines. The relative order of words cannot change. To simplify the problem, ignore spaces between words. Xiao Hong likes neat letters. Xiao Ming wants to win her heart, so he asks you to write a program to typeset the words so that the variance of the number of letters per line is minimized. Please output the minimum variance.

Line $1$: two positive integers $N, K$. Line $2$: $N$ space-separated words.

One line: a decimal number with exactly one digit after the decimal point representing the minimum variance of letters per line.

Sample Explanation: ```plain xxx xxxxx xxxx xx ``` $1 \div 2 \times ((8-7)^2+(6-7)^2) = 1$. Constraints: For $30\%$ of the testdata, $N \leq 100$, $K \leq 3$. For all testdata, $N \leq 1000$, $K \leq 100$, word length $\leq 20$. Translated by ChatGPT 5