<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:
    def beautifulSubsets(self, nums: List[int], k: int) -> int:
        if len(nums) == 1: return 1
        def checkAbsInSet(arr, target, k):
            for n in arr:
                if abs(nums[n]-nums[target]) == k:
                    return False
            return True

        allRes = []
        def backtracking(idx, curSet):
            nonlocal allRes
            if curSet:
                # print(curSet)
                pass
                # allRes.append(curSet)
            
            if idx == len(nums):
                return

            if len(curSet) > 0:
                # print(curSet)
                # print(nums[idx])
                # print(checkAbsInSet(curSet, nums[idx], k))
                # print("--")
                if checkAbsInSet(curSet, idx, k):
                    allRes.append(curSet)
                    temp = curSet
                    backtracking(idx+1, curSet + [idx])
                    curSet = temp
                backtracking(idx+1, curSet)
            else:
                allRes.append(curSet)
                temp = curSet
                backtracking(idx+1, curSet + [idx])
                curSet = temp
                
                backtracking(idx + 1, curSet)
            return

        backtracking(0, [])
        # print(allRes)
        return len(allRes)
107300