Number of Digit One

Given an integer n, count the total number of digit 1 appearing in all non-negative integers less than or equal to n.

For example:
Given n = 13,
Return 6, because digit 1 occurred in the following numbers: 1, 10, 11, 12, 13.

Hint:

public class Solution {
    public int countDigitOne(int n) {
        int count = 0;
        for (long k = 1; k <= n; k *= 10) {
            long r = n / k;
            long m = n % k;
           
            count += (r + 8)/ 10 * k + (r % 10 == 1 ? m + 1 : 0);
        }
        return count;
    }
}

System.out.println(s.countDigitOne(4135));

1:414 + 0 = 414
10:420 + 0 = 420
100:400 + 36 = 436
1000:1000 + 0 = 1000
2270