Problem B
Bachelor's Thesis
SoCCat the Undergraduate is a very studious cat. Currently, SoCCat is writing their Bachelor’s Thesis!
For SoCCat’s Final Year Project, SoCCat will write a thesis studying the behaviour of a particular operation: the catsplit.
Initially, suppose SoCCat has an array of $n$ integers $a_1, a_2, \ldots , a_ n$, and an integer $k$ ($1 \leq k \leq n$). In one catsplit operation, SoCCat will do all of the following in order:

Choose any subsequence of $a$ which consists of exactly $k$ elements.

Delete the chosen subsequence from the array $a$.

Append the values of the chosen subsequence to the beginning of the array $a$ in reverse order.
For example, for an array $a = [5, 1, 4, 2, 3]$ and integer $k = 3$, SoCCat can choose the subsequence $[1, 4, 3]$. Next, SoCCat will remove the elements $[1,4,3]$ from $a$, after which the array will become $[5,2]$. Finally, SoCCat will prepend the elements $[1, 4, 3]$ in reverse order, after which the array will become $[3,4,1,5,2]$.
SoCCat is interested in knowing the minimum possible number of inversions in the array $a$ after doing the catsplit operation between $0$ up to $100\, 000$ times. As SoCCat is busy studying other properties of the catsplit operation, they turn to you for help!
Note that you do not have to minimize the number of catsplit operations, only the number of inversions in the resulting array.
As a reminder,

$b_1, b_2, \ldots , b_ k$ is a subsequence of $a$ if and only if $b_1, b_2, \ldots , b_ k$ can be obtained from $a$ by deleting zero or more elements from it without changing the order of the remaining elements.

The inversion of an array $a$ is equal to the number of pairs $(i, j)$ such that $i < j$ and $a_ i > a_ j$.
Input
The first line of input contains two integers $n$ and $k$, denoting the number of elements in the array $a$ and the specific number of elements chosen in the subsequence for each catsplit operation ($1 \leq n \leq 100$; $1 \leq k \leq n$).
The following line contains $n$ integers $a_1, a_2, \ldots , a_ n$, denoting the elements of the array $a$ ($1 \leq a_ i \leq 100$).
Output
In the first line, output the minimum possible number of inversions in the resulting array after doing the catsplit operation between $0$ up to $100\, 000$ times.
In the second line, output $l$, denoting the number of catsplit operations SoCCat should perform to obtain the minimum number of inversions in the resulting array ($0 \leq l \leq 100\, 000$). You do not have to minimize $l$.
Each of the following $l$ lines should contain a binary string of length $n$, denoting the subsequence SoCCat should choose for that particular operation. The $i$th character of the binary string should be 1 if the $i$th element of the array is chosen for the subsequence, and 0 otherwise. Note that each binary string should therefore contain exactly $k$ 1’s.
Sample Input 1  Sample Output 1 

4 4 3 3 2 3 
1 3 1111 1111 1111 
Sample Input 2  Sample Output 2 

4 4 3 2 3 3 
1 0 
Sample Input 3  Sample Output 3 

5 2 1 2 4 3 5 
0 2 01010 01100 