You are given an integer array $A$ of length $2 \cdot N$ and integer $K$. Your should divide this array onto two arrays $B$ and $C$ with such rules:

1. The sizes of arrays $B$ and $C$ are equal to $N$.
2. Each element of array $A$ belongs to exactly one of the arrays $B$ or $C$.
3. Arrays $B$ and $C$ store indices of selected elements.
4. You must maintain the relative order of the elements (arrays $B$ and $C$ must be sorted by ascending).
5. You can't take $K$ consecutive indices in either of two arrays. (for example if $K$ is equal to $3$, then you can't take indices $[5, 6, 7]$ into arrays $B$ or $C$).

Your task is to maximize the following value: $\sum\limits_{i=1}^N f(A_{B_i}, A_{C_i})$, where $f(x, y)$ is equal to $1$ if $x < y$ and $0$ otherwise.

Input format:

First line contains two space-separated integers $N$ $(1 \leq N \leq 5 \cdot 10^4)$ and $K$ $(2 \leq K \leq min(2 \cdot N, 100))$.

Next line contains $2 \cdot N$ space-separated integers denoting the array $A$ $(1 \leq A_i \leq 10^9)$.

Output format:

In a first line output $N$ space-separated integers denoting array $B$.

In a second line output $N$ space-separated integers denoting array $C$.

Verdict and scoring:

Your score is equal to the sum of the values of all test cases.

The value of each test is calculated using this formula: $\sum\limits_{i=1}^N f(A_{B_i}, A_{C_i})$, where $f(x, y)$ is equal to $1$ if $x < y$ and $0$ otherwise.

If at least one of the rules will be violated, then your value for this test will be $0$.

Test generation plan:

Each test has own upper bound $Z$ ($1 \leq Z \leq 10^9$), denoting that every $A_i$ in this test is not exceeding $Z$.

In each test $N$ and $K$ are randomly generated (considering constraints), $Z$ is not randomly generated.

In 38% tests: all elements of array $A$ are randomly generated (considering constraints and limit $Z$).

In all other tests: while the current amount of written elements is not equal to $2 \cdot N$ do:

• take two randomly generated positive integers $X$ (considering constraints and limit $Z$) and $Y$
• $Y$ times write number $X$ (guaranteed that the current amount of written elements plus $Y$ is less than or equal to $2 \cdot N$)