Given a sorted integer array, nums, in non-decreasing order and an integer, k, determine whether it is possible to partition the array into one or more disjoint increasing subsequences, each having a length of at least k. Return true if such a partition exists; otherwise, return false.

Constraints:

• $1 \leq$ k $\leq$ nums.length$\leq 10^3$

• $1 \leq$ nums[i] $\leq 10^3$

• The nums array is sorted in non-decreasing order.