Counting the Number of Ways to Select Pots

You are given N pots each with a specific capacity. Your task is to determine the number of unique ways to select a subset of these pots such that the sum of their capacities is exactly T.

Formally, given an integer N representing the number of pots, an integer T representing the target total capacity, and an array capacities of N positive integers, find the number of subsets whose sum equals T. Mathematically, if we denote the capacities as \(a_1, a_2, \dots, a_N\), you need to count the number of index sets \(I \subseteq \{1,2,\dots,N\}\) such that:

[ \sum_{i \in I} a_i = T ]

Note that each pot can be chosen at most once.

Example:

Input: N = 4, T = 5, capacities = [1, 2, 3, 4]
Output: 2

There are two subsets that sum to 5: [1, 4] and [2, 3].

inputFormat

The first line contains two space-separated integers N and T, where N is the number of pots and T is the target capacity sum.

The second line contains N space-separated integers representing the capacities of the pots.

outputFormat

Output a single integer that is the number of unique ways to select a subset of pots such that their total capacity is exactly T.

## sample

4 5
1 2 3 4

2