You are given an integer array nums of size n and a positive integer k.

Divide the array into one or more arrays of size 3 satisfying the following conditions:

• Each element of nums should be in exactly one array.
• The difference between any two elements in one array is less than or equal to k.

Return a 2D array containing all the arrays. If it is impossible to satisfy the conditions, return an empty array. And if there are multiple answers, return any of them.

 

Example 1:

Input: nums = [1,3,4,8,7,9,3,5,1], k = 2
Output: [[1,1,3],[3,4,5],[7,8,9]]
Explanation: We can divide the array into the following arrays: [1,1,3], [3,4,5] and [7,8,9].
The difference between any two elements in each array is less than or equal to 2.
Note that the order of elements is not important.

Example 2:

Input: nums = [1,3,3,2,7,3], k = 3
Output: []
Explanation: It is not possible to divide the array satisfying all the conditions.

 

Constraints:

• n == nums.length
• 1 <= n <= 105
• n is a multiple of 3.
• 1 <= nums[i] <= 105
• 1 <= k <= 105