I have a temp table in SQL server like below
╔═══════╦═════════╦══════╦═════════╗
║Serial ║ Account ║ Due  ║ Balance ║
║1      ║ A1      ║ 1000 ║ 3100    ║
║2      ║ A1      ║ 1000 ║ 3100    ║
║3      ║ A1      ║ 1000 ║ 3100    ║
║4      ║ A1      ║ 1000 ║ 3100    ║
║1      ║ A2      ║ 100  ║ 3100    ║
║2      ║ A2      ║ 100  ║ 3100    ║    
║1      ║ B1      ║ 1000 ║ 1100    ║
║2      ║ B1      ║ 1000 ║ 1100    ║
║1      ║ B2      ║ 100  ║ 1100    ║
║2      ║ B2      ║ 100  ║ 1100    ║
╚═══════╩═════════╩══════╩═════════╝
I want to identify the rows which due would be collected. A1 and A2 Due will be collected from 3100 and B1 and B2 due will be collected from 1100.
Firstly I have used cumulative Due as following
╔═══════╔═════════╦══════╦════════════╦═════════╦
║Serial ║ Account ║ Due  ║ Cumulative ║ Balance ║
║1      ║ A1      ║ 1000 ║  1000      ║    3100 ║
║2      ║ A1      ║ 1000 ║  2000      ║    3100 ║
║3      ║ A1      ║ 1000 ║  3000      ║    3100 ║
║4      ║ A1      ║ 1000 ║  4000      ║    3100 ║
║1      ║ A2      ║ 100  ║   100      ║    3100 ║
║2      ║ A2      ║ 100  ║   200      ║    3100 ║
║1      ║ B1      ║ 1000 ║  1000      ║    1100 ║
║2      ║ B1      ║ 1000 ║  2000      ║    1100 ║
║1      ║ B2      ║ 100  ║   100      ║    1100 ║
║2      ║ B2      ║ 100  ║   200      ║    1100 ║
╚═══════╚═════════╩══════╩════════════╩═════════╝
Now I want to select following rows as output
╔═══════╔═════════╦══════╦════════════╦═════════╦
║Serial ║ Account ║ Due  ║ Cumulative ║ Balance ║  
║1      ║ A1      ║ 1000 ║  1000      ║    3100 ║
║2      ║ A1      ║ 1000 ║  2000      ║    3100 ║ 
║3      ║ A1      ║ 1000 ║  3000      ║    3100 ║  
║1      ║ A2      ║ 100  ║   100      ║    3100 ║
║1      ║ B1      ║ 1000 ║  1000      ║    1100 ║
║1      ║ B2      ║ 100  ║   100      ║    1100 ║
╚═══════╚═════════╩══════╩════════════╩═════════╩
Here is where I am stuck. How can I select those rows without using cursor or loop. All I want to do this with select statement and window functions. Thanks.
Possible Solution: If the table can be updated as following then the problem would be solved.
╔═══════╔═════════╦══════╦═══════════════════╦
║Serial ║ Account ║ Due  ║ Balance Remaining ║
║1      ║ A1      ║ 1000 ║  3100             ║
║2      ║ A1      ║ 1000 ║  2100             ║
║3      ║ A1      ║ 1000 ║  1100             ║
║4      ║ A1      ║ 1000 ║   100             ║
║1      ║ A2      ║ 100  ║   100             ║
║2      ║ A2      ║ 100  ║     0             ║
║1      ║ B1      ║ 1000 ║  1100             ║
║2      ║ B1      ║ 1000 ║   100             ║
║1      ║ B2      ║ 100  ║   100             ║
║2      ║ B2      ║ 100  ║     0             ║
╚═══════╚═════════╩══════╩═══════════════════╩
The cases Balance Remaining is equal/greater than Due we update it with difference else it will remain as before. Problem is here to update rows by partitioning between A & B.
UPDATE I am providing link with new data set to express my requirement more clearly. new dataset