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

A permutation of nums is said to form a divisible concatenation if, when you concatenate the decimal representations of the numbers in the order specified by the permutation, the resulting number is divisible by k.

Return the lexicographically smallest permutation (when considered as a list of integers) that forms a divisible concatenation. If no such permutation exists, return an empty list.

 

Example 1:

Input: nums = [3,12,45], k = 5

Output: [3,12,45]

Explanation:

Permutation Concatenated Value Divisible by 5
[3, 12, 45] 31245 Yes
[3, 45, 12] 34512 No
[12, 3, 45] 12345 Yes
[12, 45, 3] 12453 No
[45, 3, 12] 45312 No
[45, 12, 3] 45123 No

The lexicographically smallest permutation that forms a divisible concatenation is [3,12,45].

Example 2:

Input: nums = [10,5], k = 10

Output: [5,10]

Explanation:

Permutation Concatenated Value Divisible by 10
[5, 10] 510 Yes
[10, 5] 105 No

The lexicographically smallest permutation that forms a divisible concatenation is [5,10].

Example 3:

Input: nums = [1,2,3], k = 5

Output: []

Explanation:

Since no permutation of nums forms a valid divisible concatenation, return an empty list.

 

Constraints: