<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 = "3456"</code> and <code>a = 5</code>, <code>s</code> becomes <code>"3951"</code>.</li> <li>Rotate <code>s</code> to the right by <code>b</code> positions. For example, if <code>s = "3456"</code> and <code>b = 1</code>, <code>s</code> becomes <code>"6345"</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>"0158"</code> is lexicographically smaller than <code>"0190"</code> because the first position they differ is at the third letter, and <code>'5'</code> comes before <code>'9'</code>.</p> <p> </p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> s = "5525", a = 9, b = 2 <strong>Output:</strong> "2050" <strong>Explanation:</strong> 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 than "2050". </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> s = "74", a = 5, b = 1 <strong>Output:</strong> "24" <strong>Explanation:</strong> 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 than "24". </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> s = "0011", a = 4, b = 2 <strong>Output:</strong> "0011" <strong>Explanation:</strong> There are no sequence of operations that will give us a lexicographically smaller string than "0011". </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 <= s.length <= 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 <= a <= 9</code></li> <li><code>1 <= b <= s.length - 1</code></li> </ul>