Reporting consecutive substring occurrences under bounded gap constraints

We study the problem of indexing a text T[1…n]T[1…n] such that whenever a pattern P[1…p]P[1…p] and an interval [α,β][α,β] come as a query, we can report all pairs (i,j)(i,j) of consecutive occurrences of P in T   with α≤j−i≤βα≤j−i≤β. We present an O(nlog⁡n)O(nlog⁡n) space data structure with optimal O(p+k)O(p+k) query time, where k is the output size.