Problem Description

You are given a color sequence $a$ of length $n$ and a positive integer $k$. You may perform the following operation any number of times.

• Choose a subset $S$ of $\{1,2,\ldots,n\}$ and a color $c$, then change the color of every position in $S$ to $c$.

Determine the minimum number of operations needed to make the number of maximal color segments exactly $k$, and construct a solution.

If there are multiple possible constructions, you may output any.

Input Format

The first line contains two positive integers $n,k$.

The second line contains $n$ positive integers $a_i$, denoting the color sequence.

Output Format

Print the minimum number of operations $t$ on the first line.

Then print $t$ lines describing the operations in order. For each line, the first integer $s_i$ denotes the size of the chosen set, followed by $s_i$ distinct integers between $1$ and $n$ indicating the elements of the set, and finally an integer $c$ between $1$ and $n$ denoting the new color.

5 3
1 2 3 3 3

0

5 2
1 2 3 3 3

1
1 2 1

5 4
1 2 3 3 3

1
2 4 5 4

Hint

Constraints

For all test cases, $1\le k\le n\le 10^5$ and $1\le a_i\le n$.

• Special Property A: It is guaranteed that $k=1$.
• Special Property B: It is guaranteed that $k=n$.