4 integers that can be combined with + or - to make the numbers 1 through 40

There are four positive integers, a, b, c, d, which can be combined using plus or minus to get all the integers from 1 to 40 inclusive. These combinations of a, b, c, and d can involve any number of a, b, c, and d, but none of these four integers can be used more than once. That is, some possible combinations are:

However, these types of combinations are not allowed:

What are the four integers?

Probably more than a decade after I first heard this puzzle, I heard it again as the Puzzler on Car Talk #1143 (which originally aired around 2011, I think). SOLUTION

Ken Ho's home page