Given Q pairs of integers Ni, Ai (1 <= Ai, Q <= 10⁵, 4 <= N <= 100), 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".

Q = 1
Ni = 4
A1 = 16
{ 42 + 02 + 02 + 02 = 16}

Input

There's an integer Q (1 <= Q <= 10⁵) 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 <= 10⁵, 4 <= Ni <= 100). 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

Input:
1
4 16

Output:
0 0 0 4

Input:
1
4 15

Output:
1 1 2 3