#648 N Seeds

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#648 N Seeds

Authors: lacycat

Time limit: 1000 ms
Memory limit: 1024 MB
Checker: CUSTOM
Solve threshold: 100

Statement

Statement language

Consider a sequence of positive integers $a_1,a_2,\cdots$ . Let $P=a_1$ . The first $P$ terms $a_1,a_2,\cdots,a_P$ are called the seed of the sequence.

For every integer $k>P$ , the following term is defined by

a_k=\sum_{i=0}^{P-1}\left(\sum_{j=1}^{k-1-i}a_j\right)^{P-i}.

Two integers $X$ and $P$ are given. Find positive integers $a_2,a_3,\cdots,a_P$ such that for some integer satisfying .

Every input has at least one valid seed. If several seeds are valid, print any one of them.

Input

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

Output

For each case, print $P-1$ positive integers $a_2,a_3,\cdots,a_P$ forming a valid seed on one line, separated by spaces.

Constraints

$1\leq T\leq50$ .
$2\leq P\leq5$ .
$1\leq X\leq2\times10^9$ .

Subtasks

#	Score	Constraints
1	28	$P\leq3$ .
2	72	No additional constraints.

Samples

Input

Output

3
1 2
1 1 1 1

Editorial

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