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 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"`.

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 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'`.

Example 1:

    Input: s = "5525", a = 9, b = 2
    Output: "2050"
    Explanation: We can apply the following operations:
    Start:  "5525"
    Rotate: "2555"
    Add:    "2454"
    Add:    "2353"
    Rotate: "5323"
    Add:    "5222"
    Add:    "5121"
    Rotate: "2151"
    ​​​​​​​Add:    "2050"​​​​​​​​​​​​
    There is no way to obtain a string that is lexicographically smaller then "2050".

Example 2:

    Input: s = "74", a = 5, b = 1
    Output: "24"
    Explanation: We can apply the following operations:
    Start:  "74"
    Rotate: "47"
    ​​​​​​​Add:    "42"
    ​​​​​​​Rotate: "24"​​​​​​​​​​​​
    There is no way to obtain a string that is lexicographically smaller then "24".

Example 3:

    Input: s = "0011", a = 4, b = 2
    Output: "0011"
    Explanation: There are no sequence of operations that will give us a lexicographically smaller string than "0011".

Constraints:

- `2 <= s.length <= 100`
- `s.length` is even.
- `s` consists of digits from `0` to `9` only.
- `1 <= a <= 9`
- `1 <= b <= s.length - 1`