Determine/obtain/find management chain (hierarchy) for employees using SQL - sql

Question

I have a table (in an MS Access DB) with every employee at a company. The table also has a column to indicate each employee's manager. There are columns (with no data) to indicate that employee's full management chain to the CEO. I need to determine/obtain/find and fill this data using SQL (and/or VBA).
I know what needs to be done but I'm drawing a complete blank on how to do it efficiently.
I know I could go row by row but that seems so inefficient. There has to be a better way.
For example, take this table below:
+------------+-----------+----------+----------+----------+
| employeeID | managerID | manager1 | manager2 | manager3 |
+------------+-----------+----------+----------+----------+
| a | | | | |
| b | a | | | |
| c | a | | | |
| d | a | | | |
| e | b | | | |
| f | b | | | |
| g | c | | | |
| h | c | | | |
| i | d | | | |
| j | e | | | |
| k | f | | | |
| l | g | | | |
+------------+-----------+----------+----------+----------+
a has no manager (CEO)
b's manager is a
l's manager is g whose manager is c whose manager is a
etc...
So this would result in the table:
+------------+-----------+----------+----------+----------+
| employeeID | managerID | manager1 | manager2 | manager3 |
+------------+-----------+----------+----------+----------+
| a | | | | |
| b | a | a | | |
| c | a | a | | |
| d | a | a | | |
| e | b | a | b | |
| f | b | a | b | |
| g | c | a | c | |
| h | c | a | c | |
| i | d | a | d | |
| j | e | a | b | e |
| k | f | a | b | f |
| l | g | a | c | g |
+------------+-----------+----------+----------+----------+