<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:
    vector<vector<int>> result;
    void backtrack(vector<int>& nums, int index, int k, unordered_map<int, int>& count, vector<int>& subsets) {
        for(int i = index; i < nums.size(); i ++) {
            if(count[nums[i] - k] || count[nums[i]+k]) continue;
            subsets.push_back(nums[i]);
            result.push_back(subsets);
            count[nums[i]]++;
            backtrack(nums, i+1, k, count, subsets);
            subsets.pop_back();
            count[nums[i]]--;
        }
    }
    
    void print() {
        for(auto& ele: result) {
            cout<<"[";
            for(auto& num: ele) {
                cout<<num<<", ";
            }
            cout<<"]";
        }
    }
    int beautifulSubsets(vector<int>& nums, int k) {
        result.clear();
        unordered_map<int, int> count;
        vector<int> subsets;
        // int total_result = 0;
        for(int i = 0; i < nums.size(); i ++) {
            count[nums[i]] = 1;
            subsets.push_back(nums[i]);
            result.push_back(subsets);
            backtrack(nums, i+1, k, count, subsets);
            subsets.pop_back();
            count.clear();
        }

        // print();
        return result.size();
    }
};
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