Aggregating months over periods

[Ari]

Hello,

I have a number of unequal periods in a year. For this example say 5
periods. There are no actual dates here, just a raw number of months (number
format)

P1: 1
P2: 2
P3: 3.4
P4: 2
P5: 3.6

The numbers will always add up to 12.

I am searching for a formula that will tell me how many periods make up a
given number of months, moving backwards from a given period.

Example 1
Cell A1 = # Months = 5
Cell A2 = Period Beginning = 4
Cell A3 = Formula = 1.882*

*
P4 = 1 using up 2 months
P3 = .882 using up the remaining 3 months

Example 2
Cell A1 = # Months = 5.8
Cell A2 = Period Beginning = 3
Cell A3 = Formula = 2.4*

*
P3 = 1 using up 3.4 months
P2 = 1 using up 2 months
P1 = .4 using up the remaining .4 months

Any help would be very much appreciated. I have considered building an
intermediate table to help the formula, but any advice would be great.

Thanks,

Ari Blum