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`