Given integers $$$n$$$ and $$$k$$$, construct a sequence of $$$n$$$ non-negative (i.e. $$$\geq 0$$$) integers $$$a_1, a_2, \ldots, a_n$$$ such that
The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.
The only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$, $$$1 \leq k \leq 10^9$$$) — the number of non-negative integers to be printed and the sum respectively.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, output a sequence $$$a_1, a_2, \ldots, a_n$$$ on a new line that satisfies the conditions given above.
If there are multiple solutions, print any of them.
41 52 32 56 51
5 1 2 5 0 3 1 1 32 2 12
In the first test case, we have to print exactly one integer, hence we can only output $$$5$$$ as the answer.
In the second test case, we output $$$1, 2$$$ which sum up to $$$3$$$, and $$$1 | 2 = (11)_2$$$ has two $$$1$$$s in its binary representation, which is the maximum we can achieve in these constraints.
In the fourth test case, we output $$$3, 1, 1, 32, 2, 12$$$ which sum up to $$$51$$$, and $$$3 | 1 | 1 | 32 | 2 | 12 = (101\,111)_2$$$ has five $$$1$$$s in its binary representation, which is the maximum we can achieve in these constraints.
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