-----Description-----
This task requires writing a Lean 4 method that, given a binary string `s` and an integer `k`, finds the shortest contiguous substring that contains exactly `k` characters `'1'`.

Among all substrings of `s` that contain exactly `k` occurrences of `'1'`, return the one that is shortest in length. If there are multiple such substrings with the same length, return the lexicographically smallest one.

If no such substring exists, return the empty string.

-----Input-----
- s: A binary string (only consisting of characters `'0'` and `'1'`)
- k: A natural number (k ≥ 0)

-----Output-----
A string representing the shortest substring of `s` that contains exactly `k` ones. If no such substring exists, return `""`.

