shuttering subsequence problem

A and B are two strings of a finite alphabet. Let B^i be the string B concatenated i times to itself. E.g, if B = ab, then B^3 is ababab. The Stuttering Subsequence Problem is:
Given strings A and B, find the largest i such that B^i is a subsequence of A. Give an algorithm to solve the Stuttering Subsequence problem. Note, the problem asks for a subsequence check, and not a substring check.