Sum of k-Mirror Numbers

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Description

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

Solution