B'You are fed up with your messy room, so you decided to clean it up. Your room is a bracket sequence s=s_{1}s_{2} ... s_{n} of length n . Each character of this string is either an opening bracket '( ' or a closing bracket ') '. In one operation you can choose any consecutive substring of s and reverse it. In other words, you can choose any substring s[l ... r]=s_l, s_{l+1}, ... , s_r and change the order of elements in it into s_r, s_{r-1}, ... , s_{l} . For example, if you will decide to reverse substring s[2 ... 4] of string s= "((()))" it will be equal to s= "()(())". A regular (aka balanced) bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1 ' and '+ ' between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not. A prefix of a string s is a substring that starts at position 1 . For example, for s= "(())()" there are 6 prefixes: "(", "((", "(()", "(())", "(())(" and "(())()". In your opinion, a neat and clean room s is a bracket sequence that: For example, if k = 2 , then "(())()" is a neat and clean room. You want to use at most n operations to make your room neat and clean. Operations are applied one after another sequentially. It is guaranteed that the answer exists. Note that you do not need to minimize the number of operations: find any way to achieve the desired configuration in n or less operations. The first line contains integer number t ( 1 <= t <= 100 ) -- the number of test cases in the input. Then t test cases follow. The first line of a test case contains two integers n and k ( 1 <= k <= frac{n}{2}, 2 <= n <= 2000 , n is even) -- length of s and required number of regular prefixes. The second li'...