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A permutation$^{\text{∗}}$ of length $n$ is called valid if it has both of the following properties:

• It is bitonic$^{\dagger}$;
• Exactly $m$ of its subsets are cycles$^{\ddagger}$.

Let $k$ denote the number of permutations satisfying the above condition. Your task is to find and print $\min(k, 2000)$ examples of such permutations.

$^{\dagger}$ A permutation $p_1, p_2, \ldots, p_n$ is bitonic if there exists an index $i$ ($1 \leq i \leq n$) such that

• $p_{j-1} \leq p_j$ for $2 \leq j \leq i$;
• $p_j \geq p_{j+1}$ for $i \leq j \leq n-1$.

$^{\ddagger}$ A subset $C \subseteq \{ 1, 2, \ldots, n \}$ is a cycle if it satisfies the following conditions:

• $C$ is non-empty;
• if $x \in C$, then $p_x \in C$;
• $C$ is minimal, i.e., there does not exist a cycle $C'$ such that $C' \subset C$.

$^{\text{∗}}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).

Input

The input consists of a single line containing two integers $n$, $m$ ($1 \le m \leq n \le 100$) — the length of the permutations and the target number of cycles.

Output

In the first line, print a single integer $r$: the number of permutations you are going to print. Note that $r$ must be $\min(k, 2000)$ as defined in the statement.

Then, print $r$ lines. Each line must contain a bitonic permutation of length $n$, with $m$ cycles.

Note

In the example, there are $9$ valid permutations (i.e., bitonic permutations of length $6$, with $3$ cycles). For example, $[3, 5, 6, 4, 2, 1]$ is bitonic (in the above definition, $i = 3$), and it has $3$ cycles: $\{1, 3, 6\}$, $\{2, 5\}$, $\{4\}$. So you have to print $r = \min(9, 2000) = 9$ such permutations.