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.
\n\n\n
Example 1:
\n\nInput: nums = [3,12,45], k = 5
\n\nOutput: [3,12,45]
\n\nExplanation:
\n\n| Permutation | \n\t\t\tConcatenated Value | \n\t\t\tDivisible by 5 | \n\t\t
|---|---|---|
| [3, 12, 45] | \n\t\t\t31245 | \n\t\t\tYes | \n\t\t
| [3, 45, 12] | \n\t\t\t34512 | \n\t\t\tNo | \n\t\t
| [12, 3, 45] | \n\t\t\t12345 | \n\t\t\tYes | \n\t\t
| [12, 45, 3] | \n\t\t\t12453 | \n\t\t\tNo | \n\t\t
| [45, 3, 12] | \n\t\t\t45312 | \n\t\t\tNo | \n\t\t
| [45, 12, 3] | \n\t\t\t45123 | \n\t\t\tNo | \n\t\t
The lexicographically smallest permutation that forms a divisible concatenation is [3,12,45].
Example 2:
\n\nInput: nums = [10,5], k = 10
\n\nOutput: [5,10]
\n\nExplanation:
\n\n| Permutation | \n\t\t\tConcatenated Value | \n\t\t\tDivisible by 10 | \n\t\t
|---|---|---|
| [5, 10] | \n\t\t\t510 | \n\t\t\tYes | \n\t\t
| [10, 5] | \n\t\t\t105 | \n\t\t\tNo | \n\t\t
The lexicographically smallest permutation that forms a divisible concatenation is [5,10].
Example 3:
\n\nInput: nums = [1,2,3], k = 5
\n\nOutput: []
\n\nExplanation:
\n\nSince no permutation of nums forms a valid divisible concatenation, return an empty list.
\n
Constraints:
\n\n1 <= nums.length <= 131 <= nums[i] <= 1051 <= k <= 100给你一个正整数数组 nums 和一个正整数 k。
当 nums 的一个 排列 中的所有数字，按照排列顺序 连接其十进制表示 后形成的数可以 被 k 整除时，我们称该排列形成了一个 可整除连接 。
返回能够形成 可整除连接 且 字典序 最小 的排列（按整数列表的形式表示）。如果不存在这样的排列，返回一个空列表。
\n\n\n\n
示例 1：
\n\n输入: nums = [3,12,45], k = 5
\n\n输出: [3,12,45]
\n\n解释:
\n\n| 排列 | \n\t\t\t连接后的值 | \n\t\t\t是否能被 5 整除 | \n\t\t
|---|---|---|
| [3, 12, 45] | \n\t\t\t31245 | \n\t\t\t是 | \n\t\t
| [3, 45, 12] | \n\t\t\t34512 | \n\t\t\t否 | \n\t\t
| [12, 3, 45] | \n\t\t\t12345 | \n\t\t\t是 | \n\t\t
| [12, 45, 3] | \n\t\t\t12453 | \n\t\t\t否 | \n\t\t
| [45, 3, 12] | \n\t\t\t45312 | \n\t\t\t否 | \n\t\t
| [45, 12, 3] | \n\t\t\t45123 | \n\t\t\t否 | \n\t\t
可以形成可整除连接且字典序最小的排列是 [3,12,45]。
示例 2：
\n\n输入: nums = [10,5], k = 10
\n\n输出: [5,10]
\n\n解释:
\n\n| 排列 | \n\t\t\t连接后的值 | \n\t\t\t是否能被 10 整除 | \n\t\t
|---|---|---|
| [5, 10] | \n\t\t\t510 | \n\t\t\t是 | \n\t\t
| [10, 5] | \n\t\t\t105 | \n\t\t\t否 | \n\t\t
可以形成可整除连接且字典序最小的排列是 [5,10]。
示例 3：
\n\n输入: nums = [1,2,3], k = 5
\n\n输出: []
\n\n解释:
\n\n由于不存在任何可以形成有效可整除连接的排列，因此返回空列表。
\n\n\n
提示：
\n\n1 <= nums.length <= 131 <= nums[i] <= 1051 <= k <= 100mask and remainder."
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