CF847C Sum of Nestings

我们定义一个括号序列是规则的当且仅当存在某种方式可以将字符`+`和`1`插入其中使得其成为一个合法的表达式。比如`(()())`是规则的因为我们可以将它变成`((1+1)+(1+1))`的形式，而这个形式是一个合法的表达式。此外，`()()()`、`(())`、`()`也是规则的括号序列。相反，`)(`、`(()`、`())(()`不是规则的括号序列。 在这个问题中，你被给予了两个数$n$和$k$，你的任务是构建一个规则的括号序列，使得它恰好含有$n$对括号并且恰好含有$k$对嵌套。 比如，`()(())`含有$3$对括号且它的嵌套对数为$1$，而`(((())))`含有$4$对括号且它的嵌套对数为$6=3+2+1$。

The first line contains two integers $ n $ and $ k $ ( $ 1

Print the required regular bracket sequence consisting of round brackets. If there is no solution print "Impossible" (without quotes).

The first example is examined in the statement. In the second example the answer is "(((())))". The nesting of the first opening bracket is $ 0 $ , the nesting of the second is $ 1 $ , the nesting of the third is $ 2 $ , the nesting of fourth is $ 3 $ . So the total sum of nestings equals to $ 0+1+2+3=6 $ . In the third it is impossible to construct a regular bracket sequence, because the maximum possible total sum of nestings for two opening brackets equals to $ 1 $ . This total sum of nestings is obtained for the sequence "(())".