public class Solution
extends Object
2081 - Sum of k-Mirror Numbers\.
Hard
A **k-mirror number** is a **positive** integer **without leading zeros** that reads the same both forward and backward in base-10 **as well as** in base-k.
* For example, `9` is a 2-mirror number. The representation of `9` in base-10 and base-2 are `9` and `1001` respectively, which read the same both forward and backward.
* On the contrary, `4` is not a 2-mirror number. The representation of `4` in base-2 is `100`, which does not read the same both forward and backward.
Given the base `k` and the number `n`, return _the **sum** of the_ `n` _**smallest** k-mirror numbers_.
**Example 1:**
**Input:** k = 2, n = 5
**Output:** 25
**Explanation:**
The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:
base-10 base-2
1 1
3 11
5 101
7 111
9 1001
Their sum = 1 + 3 + 5 + 7 + 9 = 25.
**Example 2:**
**Input:** k = 3, n = 7
**Output:** 499
**Explanation:** The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows:
base-10 base-3
1 1
2 2
4 11
8 22
121 11111
151 12121
212 21212
Their sum = 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499.
**Example 3:**
**Input:** k = 7, n = 17
**Output:** 20379000
**Explanation:** The 17 smallest 7-mirror numbers are:
1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596
**Constraints:**
* `2 <= k <= 9`
* `1 <= n <= 30`