Execute loop calculation between two snowflake tables in SAS environment

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My goal is to calculate the final end dollar amt, the math logic is the new end dollar amt = minimum(beginning_balance_amt,net_dollar_balance), beginning balance amount = previous end balance amount

For example, I have two snowflake tables as follow:

Table A

Category Beginning Dollar AMT End Dollar AMT Month
A 1000 1000 2021-01-31
B 500 500 2023-02-28

Table B

Category Net Dollar balance Month
A 800 2021-02-28
A 2000 2021-03-31
A 300 2021-04-30
B 0 2023-03-31
B 200 2023-04-30

My expected output table is: Table C

Category Beginning Dollar AMT End Dollar AMT Month
A 1000 800 2021-02-28
A 800 800 2021-03-31
A 800 300 2021-04-30
B 500 0 2023-03-31
B 0 0 2023-04-30

The challenge for me is I have to code it in SAS with snowflake tables, and I am not sure how to do this in SAS or snowflake.

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