problem -> https://www.codechef.com/problems/ANTISM?tab=statement

In this problem, I know that a prefix and suffix approach can solve it, but I am struggling with the dynamic programming (DP) approach. I have tried to understand many solutions that use 4D or 5D DP, but I still haven’t been able to grasp them. Can anyone explain how to approach this using DP?

My recursive DP gives a TLE because it involves the sum of the subarray. Here's the structure of my recursive function:

f( i , picked_first_element , left_one_element_in_middle_after_picking , pick_one_ele_after_leaving_one_in_middle , sum_of_ele_picked_right_now , picked_anyone_ele_such_that_its_b[i]==1 ) {

// code accordingly

// gives TLE due to "sum" variable

}