Find numbers of subarray of an array whose sum is divided by 3

I got stuck in one algorithm question. Please suggest me some efficient algorithm for the below problem

Question is

Find numbers of subarrays(in range between 0

My approach:

Input:    0  5  3  8  2  1
Sum:   0  0  5  8 16 18 19
Mod 3: 0  0  2  2  1  0  1

No. of ways to chooses 0 , 1 or 2 is NC2

Problem: Is i am have asked to choose between some range i.e from 2 to 5 so array will become:

3 8 2 1

Does I have to recalculate the sum and Mod again or the original MOd array will give me a correct answer

Second Problem: What IF i change one element i.e 8 is change to 11 , How it will be effect

For the above problem I am considering using BIT dp[4][Max. Element] if mod is 0 update dp[0] if 1 update dp[1] so on How To update if VAlue at index is change