Balanced sequences X40596


Statement
 

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A sequence of numbers is d-balanced if the absolute value of the difference between any two consecutive numbers is at most d. Formally (x1, x2, … , xn) is d-balanced if for all 1 ≤ i < n it holds that | xi − xi+1 | ≤ d.

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

Input

The input consists of an integer n ≥ 1 followed by another integer d ≥ 0.

Output

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

Public test cases

  • Input

    3 1

    Output

    (1,2,3)
(3,2,1)

  • Input

    4 2

    Output

    (1,2,3,4)
(1,2,4,3)
(1,3,2,4)
(1,3,4,2)
(2,1,3,4)
(2,4,3,1)
(3,1,2,4)
(3,4,2,1)
(4,2,1,3)
(4,2,3,1)
(4,3,1,2)
(4,3,2,1)

  • Input

    1 0

    Output

    (1)
    • Information
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    Official solutions
    C++
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    C++