Small divisors of Bernoulli sums

Let ɛ= {ɛi,i ≥1} be a sequence of independent Bernoulli random variables (P{ɛi = 0} = P{ɛi = 1 } = 1/2) with basic probability space (Ω, A, P). Consider the sequence of partial sums Bn=ɛ1+...+ɛn, n=1,2..... We obtain an asymptotic estimate for the probability P{P-(Bn) > >} for >≤ne/log log n, c a positive constant.