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