# Min + Max? #1

Algebra Level 4

$\begin{cases} a^{ 2 }+b^{ 2 }+c^{ 2 }+d^{ 2 }=1 \\\\ K=ab+ac+ad+bc+bd+3cd \end{cases}$

Let 4 real numbers $a$, $b$, $c$, and $d$ satisfy the two equations above. If the minimum and maximum values of $K$ are $m$ and $M,$ respectively, what is the value of $m+M ?$