Balanced sequences

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.

Problem information

Author: Albert Oliveras

Generation: 2026-01-25T15:56:08.268Z