Kth Smallest Number in Multiplication Table

lcpy gen -n 668   # by problem number
lcpy gen -s kth_smallest_number_in_multiplication_table   # by problem name

Input: m = 3, n = 3, k = 5
Output: 3
Explanation: The 5th smallest number is 3.

Input: m = 2, n = 3, k = 6
Output: 6
Explanation: The 6th smallest number is 6.

class Solution:
    # Time: O(m * log(m * n))
    # Space: O(1)
    def find_kth_number(self, m: int, n: int, k: int) -> int:
        # Ensure the per-row count loop iterates over the smaller dimension.
        if m > n:
            m, n = n, m

        def count_le(x: int) -> int:
            return sum(min(x // i, n) for i in range(1, m + 1))

        lo, hi = 1, m * n
        while lo < hi:
            mid = (lo + hi) // 2
            if count_le(mid) < k:
                lo = mid + 1
            else:
                hi = mid
        return lo