DIstribute workload based on values across columns

I'm trying to distribute school print activity across four print servers based on the number of staff at the schools. My spreadsheet has one column with the School Name and one column with the Number of Staff. I want to distribute these values across the four Server columns without dividing any school's staff across multiple servers. The total staff per server should be as close as possible to the overall average of staff (e.g., total staff / 4 servers).

In my example, I have 26 schools named A-Z and the total staff per server should be as close to 540 as possible. Is this possible to do with an Excel formula? If not, can the be done with VBA?

Thanks for your expert reply!