Longest common substring with constant memory?

Given two strings -- how can you find the longest common substring using only constant memory?

UPDATE: The time constraints are to solve it in O(len1 * len2), like the standard dynamic-programming solu开发者_如何学Ction.

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Constant memory and no time constraints?

Just do a brute force approach: compare all possibilities, keeping just 6 integer indexes in memory: start and end for both strings, plus 2 for the longest string found yet...