<p>You are given an array <code>nums</code> of positive integers and a <strong>positive</strong> integer <code>k</code>.</p>

<p>A subset of <code>nums</code> is <strong>beautiful</strong> if it does not contain two integers with an absolute difference equal to <code>k</code>.</p>

<p>Return <em>the number of <strong>non-empty beautiful </strong>subsets of the array</em> <code>nums</code>.</p>

<p>A <strong>subset</strong> of <code>nums</code> is an array that can be obtained by deleting some (possibly none) elements from <code>nums</code>. Two subsets are different if and only if the chosen indices to delete are different.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,4,6], k = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> The beautiful subsets of the array nums are: [2], [4], [6], [2, 6].
It can be proved that there are only 4 beautiful subsets in the array [2,4,6].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1], k = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> The beautiful subset of the array nums is [1].
It can be proved that there is only 1 beautiful subset in the array [1].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>1 &lt;= nums[i], k &lt;= 1000</code></li>
</ul>

class Solution {
public:
    // Function to generate all possible subsets of the array
void generate(vector<vector<int>>& all, vector<int>& temp, vector<int>& nums, int x) {
    all.push_back(temp);
    for (int i = x; i < nums.size(); i++) {
        temp.push_back(nums[i]);
        generate(all, temp, nums, i + 1);
        temp.pop_back();
    }
}

// Function to determine the number of "beautiful" subsets based on the given condition
int beautifulSubsets(vector<int>& nums, int k) {
    vector<vector<int>> all;
    vector<int> temp;
    generate(all, temp, nums, 0);

    int count = -1;

    // Check each subset to see if it is "beautiful"
    for (const auto& subset : all) {
        bool isBeautiful = true;
        for (int i = 0; i < subset.size(); ++i) {
            for (int j = i + 1; j < subset.size(); ++j) {
                if (abs(subset[i] - subset[j]) == k) {
                    isBeautiful = false;
                    break;
                }
            }
            if (!isBeautiful) {
                break;
            }
        }
        if (isBeautiful) {
            count++;
        }
    }

    return count;
}
};
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