Small divisors of Bernoulli sums

Let ?= {?_i,i ≥1} be a sequence of independent Bernoulli random variables (P{?_i = 0} = P{?_i = 1 } = 1/2) with basic probability space (Ω, A, P). Consider the sequence of partial sums B_n=?₁+...+?_n, n=1,2..... We obtain an asymptotic estimate for the probability P{P^-(B_n) > >} for >≤n^{e/log log n}, c a positive constant.