N-square Sum! Problem? ( Medium ) 

Given Q pairs of integers Ni, Ai ( 1 <= Ai, Q <= 10^5 , 4 <= N <= 10^2 ) a, find Ni numbers whose square sums is equal to Ai. If there're more than one solution, print the one lexicographically smallest . If there's no solution, print "Impossible".

Input

 There's an integer Q ( 1 <= Q <= 10^5 ) in the first line; it stands for the number of queries. The next Q lines describe each query with two integers Ni, Ai ( 1 <= Ai <= 10^5, 4 <= Ni <= 10^2 ). Ni is the number of integers that you need to find whose sum of squares is equal to Ai.

 Output

 You have to print Q lines, each one with Ni numbers such that the sum of squares is equal to Ai. If there's no solution, you've to print "Impossible".

 Example