add-digits

#Given a non-negative integer num, repeatedly add all its digits until the result has only one digit.

#For example:

#Given num = 38, the process is like: 3 + 8 = 11, 1 + 1 = 2. Since 2 has only one digit, return it.

#Follow up:
#Could you do it without any loop/recursion in O(1) runtime? 

class Solution(object):
    
    def addDigits(self, num):
        """
        :type num: int
        :rtype: int
        """
        def imod(x, y):
            s = 1
            if x < 0:
                s = -1
            return s * ((x*s) % y)
        return 1 + imod(num-1, 9)