Table design - unknown number of column

Hello,

For a project I have a table containing products and flags.
The columns of this table are of 2 kinds :
- Not null data (id, column1, column2)
- Flags (100 different flags set to 1 or 0)

Over the time the number of flag will increase from 100 to 200 or more.

So I have 2 choices :
- Use a unique table and redesign this table and my application each
time I need to add a flag

- Split this table in 2 tables : a table containing the Not null data
and a table containing 3 columns (id, flag_name, flag_value). But in
this case how can I do a select where (flag_a=1 and flag_c=0 and
flag_k=1...) ? I would like to have 200 or more joins on the main table.

What would be the cleanest and most recommended solution ?

Thanks a lot for your help

Richard