Count Subsequences

Let's call an integer sequence *nice* if the sum of its elements is divisible by a given integer $K$. You are given an integer sequence $A_1, A_2, \ldots, A_N$. Hasan wanted to find the number of nice subsequences of this sequence. However, this problem is too easy, so Hasan decided to add an extra constraint. For an arbitrary non-empty sequence of indices $i_1 \lt i_2 \lt \ldots \lt i_L$, let's