MongoDB running sum over 3 days per ID

I have the following json file (small sample) which consists of purchase records of 4 different customers across different dates. I am required to use MongoDB/nosql to identify which customers have made at least a total of 8 new purchases over a consecutive period of 3 days.

In this case, customer ABC made 32 total purchases from 2020-05-01 to 2020-05-03 (3 consecutive days). Customer GHI also had 20 purchases from 2020-07-28 to 2020-07-30 (3 consecutive days). So my output should only contain customers ABC and GHI. What would be the code to get the output? Many thanks!

{"cust_id":"ABC", "date":"2020-05-01", "new_purchase":2},  {"cust_id":"ABC", "date":"2020-05-02", "new_purchase":16},  {"cust_id":"ABC", "date":"2020-05-03", "new_purchase":14},  {"cust_id":"ABC", "date":"2020-05-04", "new_purchase":0},  {"cust_id":"ABC", "date":"2020-05-05", "new_purchase":5},  {"cust_id":"DEF", "date":"2020-05-11", "new_purchase":3},  {"cust_id":"DEF", "date":"2020-05-12", "new_purchase":0},  {"cust_id":"DEF", "date":"2020-05-13", "new_purchase":0},  {"cust_id":"DEF", "date":"2020-05-14", "new_purchase":0},  {"cust_id":"DEF", "date":"2020-05-15", "new_purchase":1},  {"cust_id":"GHI", "date":"2020-07-28", "new_purchase":0},  {"cust_id":"GHI", "date":"2020-07-29", "new_purchase":3},  {"cust_id":"GHI", "date":"2020-07-30", "new_purchase":17},  {"cust_id":"GHI", "date":"2020-07-31", "new_purchase":0},  {"cust_id":"GHI", "date":"2020-08-01", "new_purchase":1},  {"cust_id":"JKL", "date":"2020-06-04", "new_purchase":7},  {"cust_id":"JKL", "date":"2020-06-05", "new_purchase":0},  {"cust_id":"JKL", "date":"2020-06-06", "new_purchase":0},  {"cust_id":"JKL", "date":"2020-06-07", "new_purchase":0},  {"cust_id":"JKL", "date":"2020-06-08", "new_purchase":0},  {"cust_id":"JKL", "date":"2020-06-08", "new_purchase":2}