Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example,

A = a + c (d - a b d) + e c (a + b) f + b - 1

B = a + b a c d

(where a, b, c, d, e, f are all different symbols), although it could be longer and more complicated.

I want to estimate the expression by reducing it to only the terms with zero or one symbol multiplied together because the symbols all represent small numbers, and I want a first-order approximation:

Ar = a + b - 1

Br = a

How can I automate this in Mathematica? Assume that any constants are stand-alone and don't have to be distributed.