You are given a 0-indexed integer array nums and a positive integer k.

We call an index i k-big if the following conditions are satisfied:

• There exist at least k different indices idx1 such that idx1 < i and nums[idx1] < nums[i].
• There exist at least k different indices idx2 such that idx2 > i and nums[idx2] < nums[i].

Return the number of k-big indices.

 

Example 1:

Input: nums = [2,3,6,5,2,3], k = 2
Output: 2
Explanation: There are only two 2-big indices in nums:
- i = 2 --> There are two valid idx1: 0 and 1. There are three valid idx2: 2, 3, and 4.
- i = 3 --> There are two valid idx1: 0 and 1. There are two valid idx2: 3 and 4.

Example 2:

Input: nums = [1,1,1], k = 3
Output: 0
Explanation: There are no 3-big indices in nums.

 

Constraints:

• 1 <= nums.length <= 105
• 1 <= nums[i], k <= nums.length