<p>You are given a string <code>s</code> of <strong>even length</strong> consisting of digits from <code>0</code> to <code>9</code>, and two integers <code>a</code> and <code>b</code>.</p>

<p>You can apply either of the following two operations any number of times and in any order on <code>s</code>:</p>

<ul>
	<li>Add <code>a</code> to all odd indices of <code>s</code> <strong>(0-indexed)</strong>. Digits post <code>9</code> are cycled back to <code>0</code>. For example, if <code>s = &quot;3456&quot;</code> and <code>a = 5</code>, <code>s</code> becomes <code>&quot;3951&quot;</code>.</li>
	<li>Rotate <code>s</code> to the right by <code>b</code> positions. For example, if <code>s = &quot;3456&quot;</code> and <code>b = 1</code>, <code>s</code> becomes <code>&quot;6345&quot;</code>.</li>
</ul>

<p>Return <em>the <strong>lexicographically smallest</strong> string you can obtain by applying the above operations any number of times on</em> <code>s</code>.</p>

<p>A string <code>a</code> is lexicographically smaller than a string <code>b</code> (of the same length) if in the first position where <code>a</code> and <code>b</code> differ, string <code>a</code> has a letter that appears earlier in the alphabet than the corresponding letter in <code>b</code>. For example, <code>&quot;0158&quot;</code> is lexicographically smaller than <code>&quot;0190&quot;</code> because the first position they differ is at the third letter, and <code>&#39;5&#39;</code> comes before <code>&#39;9&#39;</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;5525&quot;, a = 9, b = 2
<strong>Output:</strong> &quot;2050&quot;
<strong>Explanation:</strong> We can apply the following operations:
Start:  &quot;5525&quot;
Rotate: &quot;2555&quot;
Add:    &quot;2454&quot;
Add:    &quot;2353&quot;
Rotate: &quot;5323&quot;
Add:    &quot;5222&quot;
Add:    &quot;5121&quot;
Rotate: &quot;2151&quot;
Add:    &quot;2050&quot;​​​​​
There is no way to obtain a string that is lexicographically smaller than &quot;2050&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;74&quot;, a = 5, b = 1
<strong>Output:</strong> &quot;24&quot;
<strong>Explanation:</strong> We can apply the following operations:
Start:  &quot;74&quot;
Rotate: &quot;47&quot;
​​​​​​​Add:    &quot;42&quot;
​​​​​​​Rotate: &quot;24&quot;​​​​​​​​​​​​
There is no way to obtain a string that is lexicographically smaller than &quot;24&quot;.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;0011&quot;, a = 4, b = 2
<strong>Output:</strong> &quot;0011&quot;
<strong>Explanation:</strong> There are no sequence of operations that will give us a lexicographically smaller string than &quot;0011&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= s.length &lt;= 100</code></li>
	<li><code>s.length</code> is even.</li>
	<li><code>s</code> consists of digits from <code>0</code> to <code>9</code> only.</li>
	<li><code>1 &lt;= a &lt;= 9</code></li>
	<li><code>1 &lt;= b &lt;= s.length - 1</code></li>
</ul>

class Solution:
    def rotate(self, s, b):
        temp = s[(len(s)-b):]
        temp += s[:(len(s)-b)]
        return temp
    def add(self, s, a):
        res = ""
        for i in range(len(s)):
            if i % 2 == 0:
                res += s[i]
            else:
                res += str((int(s[i]) + a))[-1]
        return res
    def findLexSmallestString(self, s: str, a: int, b: int) -> str:
        searched = set()
        stack = [s]
        while stack:
            curr = stack.pop()
            if curr not in searched:
                searched.add(curr)
                rotate = self.rotate(curr, b)
                add = self.add(curr, a)
                stack.append(rotate)
                stack.append(add)
        return min(searched)

        

        
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