CF847C.Sum of Nestings

Recall that the bracket sequence is considered regular if it is possible to insert symbols '+' and '1' into it so that the result is a correct arithmetic expression. For example, a sequence "(()())" is regular, because we can get correct arithmetic expression insering symbols '+' and '1': "((1+1)+(1+1))". Also the following sequences are regular: "()()()", "(())" and "()". The following sequences are not regular bracket sequences: ")(", "(()" and "())(()".

In this problem you are given two integers n and k. Your task is to construct a regular bracket sequence consisting of round brackets with length 2·n with total sum of nesting of all opening brackets equals to exactly k. The nesting of a single opening bracket equals to the number of pairs of brackets in which current opening bracket is embedded.

For example, in the sequence "()(())" the nesting of first opening bracket equals to 0, the nesting of the second opening bracket equals to 0 and the nesting of the third opening bracket equal to 1. So the total sum of nestings equals to 1.

回忆一下，若能在括号序列中插入符号 '+' 和 '1'，使其成为合法的算术表达式，则该括号序列被称为正则括号序列。例如，序列 "(()())" 是正则的，因为我们可以通过插入 '+' 和 '1' 得到合法算术表达式："((1+1)+(1+1))"。以下序列也是正则括号序列："()()()"、"(())" 和 "()"。而以下序列不是正则括号序列：")("、"(()" 和 "())(()"。

本题中，你将得到两个整数 $n$ 和 $k$。你的任务是构造一个长度为 $2 \cdot n$ 的、仅由圆括号组成的正则括号序列，使得所有左括号的嵌套深度之和恰好等于 $k$。单个左括号的嵌套深度定义为：该左括号被包含在多少对括号之中（即其外层括号对的数量）。

例如，在序列 "()(())" 中，第一个左括号的嵌套深度为 $0$，第二个左括号的嵌套深度为 $0$，第三个左括号的嵌套深度为 $1$。因此，嵌套深度总和为 $1$。

The first line contains two integers n and k (1 ≤ n ≤ 3·105, 0 ≤ k ≤ 1018) — the number of opening brackets and needed total nesting.

第一行包含两个整数 $n$ 和 $k$（$1 \leq n \leq 3 \cdot 10^5$，$0 \leq k \leq 10^{18}$）——分别为左括号的数量和所需的总嵌套深度。

Print the required regular bracket sequence consisting of round brackets.

If there is no solution print "Impossible" (without quotes).

输出所需的由圆括号组成的合法括号序列。

若不存在解，则输出 "Impossible"（不带引号）。

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 "(())".

第一个示例已在题目陈述中给出。

在第二个示例中，答案为 “(((())))”。第一个左括号的嵌套深度为 0，第二个左括号的嵌套深度为 1，第三个左括号的嵌套深度为 2，第四个左括号的嵌套深度为 3。因此，嵌套深度总和为 $0 + 1 + 2 + 3 = 6$。

在第三个示例中，无法构造出合法括号序列，因为两个左括号所能达到的最大嵌套深度总和仅为 1。该最大总和由括号序列 "(())" 实现。