# Enumerating results of a variant of LCE queries

Let $$\Sigma$$ be an ordered finite alphabet. Longest Common Extension (LCE) queries are the following problem:

Input: a string $$w$$ of size $$n$$
Query: two integers $$i$$ and $$j$$ such that $$0 < i \leq n$$ and $$0 < j \leq n$$
Output: $$\max \{ k, w[i..i+k] = w[j..j+k] \}$$

where $$w[i]$$ is the $$i$$-th character of $$w$$ (starting from $$1$$) and $$w[i..j] = w[i] w[i+1] \dots w[j]$$.

LCE queries are solvable in $$O(1)$$ for any $$i$$ and $$j$$ after a linear preprocessing of $$w$$.

I want to solve a variant of this problem (one might call it Mirror LCE queries):

Input (same as before): a string $$w$$ of size $$n$$
Query (same as before): two integers $$i$$ and $$j$$ such that $$0 < i \leq n$$ and $$0 < j \leq n$$
Output : $$\{ k, w[i-k..i] = w[j..j+k] \}$$

Are Mirror LCE queries enumerable in linear preprocessing constant-delay ?

Note: by linear preprocessing constant-delay, I mean the following: the algorithm is first given $$w$$ and has linear time to produce a data structure $$D$$. This data structure can then be used with any $$i$$ and $$j$$ to enumerate all the corresponding $$k$$s with no duplicates with $$O(1)$$ time between two consecutive answers.