package main

import "slices"

func smallestDistancePair(nums []int, k int) int {
	pairsWithMaxDistance := func(distance int) int {
		count := 0

		left := 0
		for right := 0; right < len(nums); right++ {
			for nums[right]-nums[left] > distance {
				left++
			}

			count += right - left
		}

		return count
	}

	slices.Sort(nums)

	low, high := 0, nums[len(nums)-1]-nums[0]

	for low < high {
		mid := (low + high) / 2
		count := pairsWithMaxDistance(mid)

		if count < k {
			low = mid + 1
		} else {
			high = mid
		}
	}

	return low
}