class Solution {
 public:
  int smallestDistancePair(vector<int>& nums, int k) {
    sort(begin(nums), end(nums));

    int l = 0;
    int r = nums.back() - nums.front();

    while (l < r) {
      const int m = (l + r) / 2;
      if (pairDistancesNoGreaterThan(nums, m) >= k)
        r = m;
      else
        l = m + 1;
    }

    return l;
  }

 private:
  int pairDistancesNoGreaterThan(const vector<int>& nums, int m) {
    int count = 0;
    int j = 1;
    // for each index i, find the first index j s.t. nums[j] > nums[i] + m,
    // so pairDistancesNoGreaterThan for index i will be j - i - 1
    for (int i = 0; i < nums.size(); ++i) {
      while (j < nums.size() && nums[j] <= nums[i] + m)
        ++j;
      count += j - i - 1;
    }
    return count;
  }
};

class Solution {
  public int smallestDistancePair(int[] nums, int k) {
    Arrays.sort(nums);

    int l = 0;
    int r = nums[nums.length - 1] - nums[0];

    while (l < r) {
      final int m = (l + r) / 2;
      if (pairDistancesNoGreaterThan(nums, m) >= k)
        r = m;
      else
        l = m + 1;
    }

    return l;
  }

  private int pairDistancesNoGreaterThan(int[] nums, int m) {
    int count = 0;
    int j = 1;
    // for each index i, find the first index j s.t. nums[j] > nums[i] + m,
    // so pairDistancesNoGreaterThan for index i will be j - i - 1
    for (int i = 0; i < nums.length; ++i) {
      while (j < nums.length && nums[j] <= nums[i] + m)
        ++j;
      count += j - i - 1;
    }
    return count;
  }
}

class Solution:
  def smallestDistancePair(self, nums: List[int], k: int) -> int:
    nums.sort()

    l = 0
    r = nums[-1] - nums[0]

    while l < r:
      m = (l + r) // 2
      count = 0

      j = 0
      for i in range(len(nums)):
        while j < len(nums) and nums[j] <= nums[i] + m:
          j += 1
        count += j - i - 1

      if count < k:
        l = m + 1
      else:
        r = m

    return l