<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:
    int f(int i,int mask,vector<int>&nums,vector<vector<int>>&dp,int &k){
        if(i<0){
            
            if(mask!=0)return 1;
            return 0;
        }
        if(dp[i][mask]!=-1)return dp[i][mask];
        int nottake=f(i-1,mask,nums,dp,k);
        int take=0;
        int f1=0;
        for(int j=0;j<31;j++){
            if((mask&(1<<j))!=0){
                if(abs(nums[i]-nums[j])==k){
                    f1=1;
                    break;
                }
            }
        }
        if(f1==0){
            mask=mask|(1<<i);
            take=f(i-1,mask,nums,dp,k);
        }
        return dp[i][mask]=take+nottake;
    }
    int beautifulSubsets(vector<int>& nums, int k) {
        int n=nums.size();
        int mask=0;
        vector<vector<int>> dp(n,vector<int>(((1<<n)),-1));
        return f(n-1,mask,nums,dp,k);
        
    }
};
191567