Minimal d-exponent

Let $p$ be a prime number. Take an integer i \ge 0 and raise all integers from $0$ to p-1 to the power 2^i modulo $p$. Denote the resulting set as S_i, and let d_i be the number of elements in this set. The $d$-exponent of $p$ is defined as the minimum of all d_i over all possible i \ge 0.

You are given two positive integers $A$ and $B$. Among all primes in the interval $[A,B]$, find the minimum possible $d$-exponent. It is guaranteed that there is at least one prime number in $[A,B]$.