You are given an integer array nums, which contains distinct elements and an integer k.

A subset is called a k-Free subset if it contains no two elements with an absolute difference equal to k. Notice that the empty set is a k-Free subset.

Return the number of k-Free subsets of nums.

A subset of an array is a selection of elements (possibly none) of the array.

 

Example 1:

Input: nums = [5,4,6], k = 1
Output: 5
Explanation: There are 5 valid subsets: {}, {5}, {4}, {6} and {4, 6}.

Example 2:

Input: nums = [2,3,5,8], k = 5
Output: 12
Explanation: There are 12 valid subsets: {}, {2}, {3}, {5}, {8}, {2, 3}, {2, 3, 5}, {2, 5}, {2, 5, 8}, {2, 8}, {3, 5} and {5, 8}.

Example 3:

Input: nums = [10,5,9,11], k = 20
Output: 16
Explanation: All subsets are valid. Since the total count of subsets is 24 = 16, so the answer is 16. 

 

Constraints:

• 1 <= nums.length <= 50
• 1 <= nums[i] <= 1000
• 1 <= k <= 1000