Radical radicals

The sequence $\{u_n\}\subset\mathbb{Z}^+$ on $n\in\mathbb{Z}^+$ is defined by $u_1=1$ and

$\sqrt{u_n+\sqrt{u_{n-1}+\sqrt{u_{n-2}+\sqrt{...+\sqrt{u_2+\sqrt{u_1}}}}}}=n$

The sequence $\{v_n\}\subset\mathbb{Z}^+$ on $n\in\mathbb{Z}^+$ is defined by $v_1=1$ and

$\sqrt[3]{v_n+\sqrt[3]{v_{n-1}+\sqrt[3]{v_{n-2}+\sqrt[3]{...+\sqrt[3]{v_2+\sqrt[3]{v_1}}}}}}=n$

Let:

• $A$ = the last digit of $u_{2016}$
• $B$ = $\text{min}(k)$ such that $u_k-k \geq 2016$
• $C$ = $\text{min}(k)$ such that $v_k-u_k \geq 2016$

Find $A+B+C$ .