Sum Of K Mirror Numbers · Interview Problem

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Leetcode

Medium

Math

Number Theory

Strings

Recursion

Google

Sum Of K Mirror Numbers

Find the sum of the first $n$ positive integers that are palindromic in base 10 and also in base $k$ .

Acceptance 100%

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Problem Statement

Problem

A positive integer is called $k$ -mirror if it is a palindrome in both base 10 and base $k$ .

Given two integers $n$ and $k$ , return the sum of the first $n$ positive integers that are $k$ -mirror numbers.

A number is a palindrome if it reads the same forward and backward in its base representation.

Clarification

You should consider positive integers only, and the numbers should be counted in increasing order.

Goal

Generate the first $n$ numbers that satisfy both palindrome conditions, then return their sum.

Input Format

One line containing two integers $n$ and $k$ .
$n$ is the count of $k$ -mirror numbers to find.
$k$ is the base used for the second palindrome check.

Output Format

Return a single integer: the sum of the first $n$ $k$ -mirror numbers.

Constraints

$1 \le n$
$2 \le k$
The numbers searched are positive integers.
The answer fits in a 64-bit signed integer for the intended test data.

Examples

Sample cases returned by the problem API.

Example 1

Input

n = 5, k = 2

Output

Explanation

The first five positive integers that are palindromic in both base 10 and base 2 are 1, 3, 5, 7, and 9. Their sum is 25.

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