invariant of bin packing We are given an array of integers and a number K. We need to pack these integers into bins. The condition is that we have to use exactly K number of bins and each bin should have equal capacity. We need to find the size of bin such that wastage of unused bin is minimized.

Is this problem polynomial time solvable?
Since the number of bins is fixed, the problems boils down to a job shop scheduling with atomic jobs. See https://en.wikipedia.org/wiki/Job_shop_scheduling#Atomic_jobs

A solution is given by $\max\{ 1/m \sum_{i=1}^n t_i, max_i t_i  \}$
where $t_i$ represents the $i$th integer and $m$ represent the set length. The wiki reference above includes a paper with the proof.

EDIT after request on polynomial time
Since it's equivalent to the partition problem, which is NP-hard, this problem is also NP-hard and therefore not solvable in polynomial time.