postgresql – Roll up aggregate until column change

Not sure how to explain this properly but here goes.

I a table with rows that are related to each other and I want to aggregate them based on a sort order until the value in one column has a certain value that would reset the group.

Sample table:

|cust_id|price  |timestamp       |type|
|-------|-------|-------         |----|
|1      |10     |2021-01-29 12:32|1   |
|1      |20     |2021-01-29 12:33|2   |
|1      |15     |2021-01-29 12:34|2   |
|2      |10     |2021-01-29 12:33|1   |
|1      |20     |2021-01-29 12:34|1   |
|2      |10     |2021-01-29 12:35|2   |

Wanted result:

|cust_id|price  |timestamp       |type|
|-------|-------|-------         |----|
|1      |45     |2021-01-29 12:32|1   |
|2      |20     |2021-01-29 12:33|1   |
|1      |20     |2021-01-29 12:34|1   |

So the input table would be sorted by timestamp and then grouped by cust id, the price is aggregated until the next occurrence where type is 1 which would indicate a new group. Type here is just one and two, but can in reality have a lot of different values.

I have not figured out a good way of accomplishing this so any pointers is appreciated.