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Maximum Frequency of an Element After Performing Operations II

Hard

You receive an integer array nums and two integers k and numOperations.

You must perform an operation numOperations times on nums, where in each operation you:

  • Select an index i that was not selected in any previous operations.

  • Add an integer in the range [-k, k] to nums[i].

Produce the maximum possible frequency of any element in nums after performing the operations.

Example 1

Input: nums = [1,4,5], k = 1, numOperations = 2

Output: 2

Explanation: We can achieve a maximum frequency of two by:

  • Adding 0 to nums[1], after which nums becomes [1, 4, 5].

  • Adding -1 to nums[2], after which nums becomes [1, 4, 4].

Example 2

Input: nums = [5,11,20,20], k = 5, numOperations = 1

Output: 2

Explanation: We can achieve a maximum frequency of two by:

  • Adding 0 to nums[1].

Constraints

  • 1 <= nums.length <= 10^5
  • 1 <= nums[i] <= 10^9
  • 0 <= k <= 10^9
  • 0 <= numOperations <= nums.length

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