Lexicographically Smallest String After Applying Operations

You are given a string s of even length consisting of digits from 0 to 9, and two integers a and b.

You can apply either of the following two operations any number of times and in any order on s:

• Add a to all odd indices of s (0-indexed). Digits past 9 are cycled back to 0.
• Rotate s to the right by b positions.

Return the lexicographically smallest string you can obtain by applying the above operations any number of times on s.

A string a is lexicographically smaller than a string b of the same length if, in the first position where a and b differ, string a has a character that appears earlier in the alphabet than the corresponding character in b.