Zombie and the Caves

There are $N$ caves in a row, numbered $1$ through $N$. For each valid $i$, the *radiation power* in the $i$-th cave is $C_i$. Originally, the *radiation level* in each cave was $0$. Then, for each valid $i$, the radiation power in cave $i$ increased the radiation levels in the caves $i-C_i, \ldots, i+C_i$ inclusive (if they exist) by $1$, so all the caves are radioactive now. Radiation is not