Given real numbers $b_0,b_1,\ldots,b_{2019}$ with $b_{2019}\neq0$, let $z_1,z_2,\ldots,z_{2019}$ be the roots in the complex plane of the polynomial $$P(z)=\sum_{k=0}^{2019}b_kz^k.$$ Let $\mu=(|z_{1}|+\cdots+|z_{2019}|)/2019$ be the average of the distances from $z_1,z_2,\ldots,z_{2019}$ to the origin. Determine the largest constant $M$ such that $\mu\geq M$ for all choices of $b_0,b_1,\ldots,b_{2019}$ that satisfy $$1\leq b_0<b_1<b_2<\cdots<b_{2019}\leq2019.$$ The original answer is in the form $M=a^{b/ c}$, please provide the value of a+ b+c .

Let's think step by step and output the final answer within \boxed{}.
user