Carrot Collection

Deep in a forest live a bear and a rabbit. The forest has $N$ clearings, numbered from $1$ to $N$. Clearing $i$ has $A_i$ carrots growing in it. The bear patrols several zones of the forest - specifically, you are given integers $L$ and $R$, such that the bear patrols clearings $L, L+1, L+2, \ldots, R$. It is guaranteed that either $L \gt 1$ or $R \lt N$, i.e. there exists at least one clear