If I have an array of sorted numbers and every object is one of the numbers or multiplication. For example if the sorted array is [1, 2, 7] then the set is {1, 2, 7, 1*2, 1*7, 2*7, 1*2*7}. As you can see if there's n numbers in the sorted array, the size of the set is 2^n-1.

My question is how can I find for a given sorted array of n numbers all the objects in the set so that the objects is in a given interval. For example if the sorted array is [1, 2, 3 ... 19, 20] what is the most efficient algorithm to find the objects that are larger than 1000 and less than 2500 (without calculating all the 2^n-1 objects)?