---{"category_name":"easy","problem_code":"ANKPAREN","problem_name":"Longest non regular parentheses sub-sequence","languages_supported":{"0":"ADA","1":"ASM","2":"BASH","3":"BF","4":"C","5":"C99 strict","6":"CAML","7":"CLOJ","8":"CLPS","9":"CPP 4.3.2","10":"CPP 4.9.2","11":"CPP14","12":"CS2","13":"D","14":"ERL","15":"FORT","16":"FS","17":"GO","18":"HASK","19":"ICK","20":"ICON","21":"JAVA","22":"JS","23":"LISP clisp","24":"LISP sbcl","25":"LUA","26":"NEM","27":"NICE","28":"NODEJS","29":"PAS fpc","30":"PAS gpc","31":"PERL","32":"PERL6","33":"PHP","34":"PIKE","35":"PRLG","36":"PYPY","37":"PYTH","38":"PYTH 3.4","39":"RUBY","40":"SCALA","41":"SCM chicken","42":"SCM guile","43":"SCM qobi","44":"ST","45":"TCL","46":"TEXT","47":"WSPC"},"max_timelimit":1,"source_sizelimit":50000,"problem_author":"code_master01","problem_tester":"rubanenko","date_added":"9-06-2015","tags":{"0":"basic","1":"code_master01","2":"cook59","3":"easy","4":"pattern","5":"stack"},"editorial_url":"http://discuss.codechef.com/problems/ANKPAREN","time":{"view_start_date":1434911400,"submit_start_date":1434911400,"visible_start_date":1434911400,"end_date":1735669800},"layout":"problem"}---<span class="solution-visible-txt">All submissions for this problem are available.</span><h3> Read problems statements in <a target="_blank" href="http://www.codechef.com/download/translated/COOK59/mandarin/ANKPAREN.pdf">Mandarin Chinese</a> and <a target="_blank" href="http://www.codechef.com/download/translated/COOK59/russian/ANKPAREN.pdf">Russian</a> as well.</h3><p>Chef has recently learnt about sequences of parentheses. These are special sequences that contain only the characters <em>'('</em> and <em>')'</em>.</p><p>A regular parentheses sequence follows the following definition:</p><ul><li>An empty sequence is regular</li><li>If <strong>S</strong> is a regular sequence, then <strong>(S)</strong> is also regular</li><li>If <strong>A</strong> and <strong>B</strong> represent two regular sequences, then their concatenation <strong>AB</strong> is also regular.</li></ul><p>Therefore, the sequences <strong>(), ()()</strong> and <strong>(())()</strong> are regular, while <strong>()(, )</strong> and <strong>))()</strong> are non-regular.</p><p>Now, you need to find the longest subsequence of the given sequence which is non-regular. Amongst all such <strong>distinct</strong> answers, output the lexicographically <strong>K<sup>th</sup></strong> amongst them. If the number of distinct subsequences with maximum length is less than <strong>K</strong>, please output -1 instead.</p><h3>Input:</h3><p>The first line contains a single integer <strong>T</strong>, denoting the number of test cases to follow.<br />Each of the test cases have exactly two lines, the first contains the parentheses sequence and the second contains the value of <b>K</b>.</p><h3>Output:</h3><p>Output exactly <strong>T</strong> lines, each containing answer to the corresponding query.</p><h3>Constraints:</h3><ul><li>1 ≤ <strong>T</strong> ≤ 10</li><li>1 ≤ |<strong>S</strong>| ≤ 10<sup>5</sup></li><li>1 ≤ <strong>K</strong> ≤ 10<sup>9</sup></li></ul><h3>Example:</h3><p><strong>Sample Input:</strong></p><pre>5()2(()1(()2(())2(())3</pre><p><strong>Sample Output:</strong></p><pre>)(()-1())-1</pre><h3>Explanation:</h3><p><strong>Case 1:</strong>Following are the subsequences:</p><pre>Length Subsequence Regular/Non-Regular1 ( Non-regular1 ) Non-regular2 () Regular</pre><p>There are two non-regular subsequences of equal length:'(' and ')'.<br />We are asked for the lexicographically 2nd, so output should be ')'.</p><p><strong>Case 2:</strong>Following are the subsequences:</p><pre>Length Subsequence Regular/Non-Regular1 ( Non-Regular1 ) Non-Regular2 (( Non-Regular2 () Regular3 (() Non-Regular</pre><p>In this case, there are non-regular subsequences of lengths 1, 2, and 3. But, as 3 is the maximum among these, we choose, <strong>(()</strong>.</p><p><strong>Case 3:</strong><br />The string is same as Case 2, and we realize that there is only one subsequence of the maximum length 3, thus we must output -1.</p><p><strong>Case 4:</strong><br />We can find that following subsequences have maximum length and are non-regular.</p><pre>Length Subsequence3 ())3 (()</pre><p>In lexicographical order, we have following subsequences: [ ((), ()) ]<br />The query asks for 2nd subsequence, thus the required output is ()).</p><p><strong>Case 5:</strong><br />This is the same sequence as last case, and we know that there are exactly 2 distinct subsequences of maximum length. Thus, answer should be -1.</p><h3>Notes:</h3><ul><li>A subsequence of a given sequence <strong>A</strong> is a non-empty sequence obtained by removing zero or more characters from <strong>A</strong>. It does not need to be contiguous.</li><li>A sequence <strong>A</strong> is called different from another sequence <strong>B</strong>, if there exists an integer <strong>k</strong>, such that 1 ≤ <strong>k</strong> ≤ <strong>N</strong> (<strong>N </strong> is the length of both sequences), and <strong>A<sub>k</sub> != B<sub>k</sub>.</strong></li><li>Consider two different <b>N</b>-length sequences, <b>A</b> and <b>B</b>. Let <b>k</b> be the smallest integer such that <strong>A[k] != B[k]</strong> and 1 ≤ <b>k</b> ≤ <b>N</b>. If <b>A[k] < B[k]</b>, then <b>A</b> is said to be lexicographically smaller than <b>B</b>, and vice-versa.</li></ul>