Given an integer array nums sorted in non-decreasing order and an integer k, return true if this array can be divided into one or more disjoint increasing subsequences of length at least k, or false otherwise.

 

Example 1:

Input: nums = [1,2,2,3,3,4,4], k = 3
Output: true
Explanation: The array can be divided into two subsequences [1,2,3,4] and [2,3,4] with lengths at least 3 each.

Example 2:

Input: nums = [5,6,6,7,8], k = 3
Output: false
Explanation: There is no way to divide the array using the conditions required.

 

Constraints:

• 1 <= k <= nums.length <= 105
• 1 <= nums[i] <= 105
• nums is sorted in non-decreasing order.