The correct bracket sequence (also known as a balanced bracket sequence or correct parenthesis sequence) is a string consisting of only brackets $("("$ and $")")$ such that this sequence when inserted certain numbers and mathematical operations give a valid mathematical expression. For instance, $(())()$ is a correct bracket sequence and $1+(2-(3*4)/6)+(7-8)$ is one of the possible expressions that can be obtained from it but $())$ is not a correct bracket sequence. An empty string is a correct bracket sequence as well.

An almost correct bracket sequence is a string that consists of only brackets that can be turned into a correct bracket sequence by removing exactly one bracket from it. For instance, $())$ is an almost correct bracket sequence because removing any of closing brackets turns it into a correct bracket sequence $()$ but $((($ is not an almost correct bracket sequence. Obviously, the length of each almost correct bracket sequence is an odd number.

You are given two integers $n$ and $k$. Consider all almost correct bracket sequences of length $n$ and order these sequences lexicographically assuming that $(\ <\ )$). Determine the $k^{th}$ sequence in the ordering sequence or report that the number of almost correct bracket sequences of length $n$ is less than $k$.

Input format

• First line: $T$ denoting the number of test cases
• Next $T$ lines: Two integers $n$ and $k$ the length of the required almost correct bracket sequence and its position in lexicographic order

Output format

For each test case, print the answer in a separate line. If there are less than $k$ almost correct bracket sequences of length $n$, then print Impossible. Otherwise, print the required sequence.

Constraints

$1 \le T \le 5000$

$1 \le n \le 65$, $n$ is odd

$1 \le k \le 2^{63} - 1$