Lexicographically Smallest String After Applying Operations

You receive 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 post 9 are cycled back to 0 . For example, if s = "3456" and a = 5 , s becomes "3951" .

• Rotate s to the right by b positions. For example, if s = "3456" and b = 1 , s becomes "6345" .

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

A text 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 letter that appears earlier in the alphabet than the corresponding letter in b . For example, "0158" is lexicographically smaller than "0190" because the first position they differ is at the third letter, and '5' comes before '9' .