Question 3 long challenge division 2

Chef is given a sequence of prime numbers A1,A2,…,AN. This sequence has exactly 2N subsequences. A subsequence of A is good if it does not contain any two identical numbers; in particular, the empty sequence is good.

Chef has to find the number of good subsequences which contain at most K numbers. Since he does not know much about subsequences, help him find the answer. This number could be very large, so compute it modulo 1,000,000,007.
I am telling u my approach, first i will make an array of strings, take input as numbers, sort this array to see which numbers are repeating and then ill calculate how many numbers are there,say k(considering similar numbers as one), then for atmost k combinations ill select kC1 (for selecting combinations of 1)+1(empty combination)+kC2-(all the repeting cases of 2)+kC3-(all repeting cases of 3)+…+kCk
Is my logic correct??, please initiate a chat after reading this