Balanced sequences X40596

A sequence of numbers is $d$-balanced if the absolute value of the difference between any two consecutive numbers is at most $d$. Formally $(x_1, x_2, \ldots , x_n)$ is $d$-balanced if for all $1 \leq i < n$ it holds that $\lvert x_i - x_{i+1} \rvert \leq d$.

Write a program that, given an integer $n\geq 1$ and an integer $d \geq 0$, writes all $d$-balanced sequences that can be obtained by reordering the sequence $(1, 2, \ldots , n)$.

Input

The input consists of an integer $n \geq 1$ followed by another integer $d \geq 0$.

Output

Write all $d$-balanced sequences that can be obtained by reordering the sequence $(1, 2, \ldots , n)$. You can write the sequences in any order.