Smallest Range Covering Elements from K Lists

Hard

Description

Given k lists of sorted integers, find the smallest range [a, b] such that b - a is minimal and the range includes at least one number from each list.

Examples

Input:nums = [[4,10,15,24,26],[0,9,12,20],[5,18,22,30]]
Output:[20,24]
Explanation:

Smallest range covering all lists.

Input:nums = [[1]]
Output:[1]
Explanation:

Minimal case with a single-element matrix.

Input:nums = [[1,2,3],[1,2,3],[1,2,3]]
Output:[1,1]
Explanation:

When all lists have identical elements, the smallest range is just picking the same element from each list. Picking 1 from each list gives range [1,1] with size 0, which is the minimum possible.

Constraints

  • 3 ≤ nums.length ≤ 3500

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