Kth Smallest Number in Multiplication Table

class Solution(object):
    def findKthNumber(self, m, n, k):
        """
        :type m: int
        :type n: int
        :type k: int
        :rtype: int
        """
        def helper(p):
            res = 0
            for i in range(1, m+1):
                res += min(p//i, n)
            return res

        beg = 1
        end = m*n
        mid = (beg + end) // 2
        while beg <= end:
            if helper(mid) < k:
                beg = mid + 1
            else:
                end = mid - 1
            mid = (beg + end) // 2

        return beg