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 = 2Output:"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 = 1Output:"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 = 2Output:"0011"Explanation:There are no sequence of operations that will give us a lexicographically smaller string than "0011".

**Example 4:**

Input:s = "43987654", a = 7, b = 3Output:"00553311"

**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`

class Solution {
public String findLexSmallestString(String s, int a, int b) {
}
}