Untitled

def subsetSum(A, k):
    n = len(A)
    
    # Calculate the total sum range considering both positive and negative numbers
    sum_min = sum(x for x in A if x < 0)
    sum_max = sum(x for x in A if x > 0)
    
    # DP table: Use a dictionary to handle possible negative indices
    T = [{} for _ in range(n + 1)]
    
    # Base case: There's always a subset with sum 0 (empty subset)
    T[0][0] = True
    
    # Fill the DP table
    for i in range(1, n + 1):
        for current_sum in range(sum_min, sum_max + 1):
            if current_sum in T[i - 1]:
                # Case 1: Exclude the current element
                T[i][current_sum] = T[i - 1][current_sum]
                # Case 2: Include the current element
                new_sum = current_sum + A[i - 1]
                T[i][new_sum] = True
    
    # Return whether a subset with sum `k` exists
    return T[n].get(k, False)

# Test case
A = [12, 1, 61, 5, 9, -3, -1]
k = 72
print(subsetSum(A, k))  # Should return True or False based on the subset