Cherry isn't feeling well right now as she found a problem that she couldn't solve. So she started to listen to Isn't It Strange? and you, to make her happy, have to solve the problem for her.
You are given an integer $L$
. You have to find an integer sequence $a_1, a_2, \ldots, a_n$
such that the following conditions are satisfied:
$n$
, is positive and doesn't exceed $1000$
.$i$
, $1 \le a_i \le 1000$
.$S$
which contains $\frac{n * (n + 1)}{2}$
integers: for each $1 \le l \le r \le n$
, $LIS(l, \, r)$
belongs to $S$
. Then, the LCM of the elements of $S$
is exactly equal to $L$
.Here, $LIS(l, r)$
is the length of the longest increasing subsequence of the sequence $a_l, a_{l + 1}, \ldots, a_r$
.
The longest increasing subsequence of a sequence $b_1, b_2, \ldots, b_m$
is the longest sequence of valid indices $i_1, i_2, \ldots, i_k$
such that $i_1 \lt i_2 \lt \ldots \lt i_k$
and $b_{i_1} \lt b_{i_2} \lt \ldots \lt b_{i_k}$
.
The first line of the input contains a single integer $t(1 \le t \le 100)$
denoting the number of test cases. The description of $t$
test cases follows.
The first and only line of each test case contains an integer $L(1 \le L \le 10^{18})$
.
For each test case, print the answer in the following way:
$n$
. On the next line, print $n$
space-separated integers $a_1, a_2, \ldots, a_n$
.Input | Output |
---|---|
2 6 20 | 5 4 2 3 2 5 -1 |
In the first test case, For the sequence
So the multiset |