so i am working on a kata :

Digitwise addition is a special kind of addition where instead of adding 1 normally to the number, it adds 1 to every digit of that number. If the digit is a 9, we replace it with a 10 without carrying over to the next digit.

Examples
123 -> 234

Task
Program a function that takes two numbers, n and k, and outputs the number of digits in n after applying Digitwise addition k times. Since the answer can be very large, return the answer modulo 1_000_000_007.

Your solution is expected to be O(klogn).

AND MY SOLUTION IS :

import sys
MOD = 10**9 + 7 

sys.set_int_max_str_digits(0)

def d2a(digits):

  arr= list(map(int,str(digits)))
  return arr


def a2d(arr):
  length=len(arr)
  digit=""

  for i in range(length):
    digit+=str(arr[i])
  return int(digit)


def add(n):
  return n+1


def digitwise_addition(digit, K):
  for i in range(K):
    #CONVERTING INTO ARRAY
    arr=d2a(digit)
    #ADDING 1 INTO ALL NUMBERS FROM ARRAY
    arr=list(map(add,arr))
    #CONVERTING ARRAY INTO DIGIT
    digit=a2d(arr)

  arr=d2a(digit)
  return len(arr) %MOD

problem : it passes all the calculations ,but when K is large ,it asks to exceed limit ,and if exceeded, it says : code timeout ,KINDLY HELP ME OUT