Beautiful Arrangement II

arraymath

Problem Statement

Given two integers n and k , construct a list answer that contains n different positive integers ranging from 1 to n and obeys the following requirement:

Suppose this list is answer = [a _1 , a _2 , a _3 , ... , a _n ] , then the list [|a _1 - a _2 |, |a _2 - a _3 |, |a _3 - a _4 |, ... , |a _n-1 - a _n |] has exactly k distinct integers.

Return the list answer . If there multiple valid answers, return any of them .

Examples

Example 1

Input: n = 3, k = 1
Output: [1,2,3]
The [1,2,3] has three different positive integers ranging from 1 to 3, and the [1,1] has exactly 1 distinct integer: 1

Example 2

Input: n = 3, k = 2
Output: [1,3,2]
The [1,3,2] has three different positive integers ranging from 1 to 3, and the [2,1] has exactly 2 distinct integers: 1 and 2.

Constraints

1 <= k < n <= 10 ^4

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMath