Given a sorted integer array nums and an integer n, add/patch elements to the array such that any number in the range [1, n] inclusive can be formed by the sum of some elements in the array.

Return the minimum number of patches required.

  Example 1:

Input: nums = [1,3], n = 6 Output: 1 Explanation: Combinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4. Now if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,3], [1,2,3]. Possible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6]. So we only need 1 patch.

Example 2:

Input: nums = [1,5,10], n = 20 Output: 2 Explanation: The two patches can be [2, 4].

Example 3:

Input: nums = [1,2,2], n = 5 Output: 0

  Constraints:

1 <= nums.length <= 1000
1 <= nums[i] <= 10⁴
nums is sorted in ascending order.
1 <= n <= 2³¹ - 1