Minimum Threshold for Inversion Pairs Count

Given an array and a target K, find the smallest threshold T such that when elements are classified by the threshold (e.g., "large" if >T and "small" otherwise) the number of inversion pairs (i<j with a[i] considered larger than a[j]) is ≤ K. The problem requires searching over candidate thresholds (typically via binary search) and efficiently counting inversion pairs for each candidate.