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Minimum Elements to Add to Form a Given Sum

You are given an integer array nums and two integers limit and goal.

You are given an integer array nums and two integers limit and goal. The array nums has an interesting property that abs(nums[i]) <= limit.

Return the minimum number of elements you need to add to make the sum of the array equal to goal. The array must maintain its property that abs(nums[i]) <= limit.

Note that abs(x) equals x if x >= 0, and -x otherwise.

Minimum Elements to Add to Form a Given Sum diagram

Example 1

Input: nums = [1,-1,1], limit = 3, goal = -4

Output: 2

Explanation: You can add -2 and -3, then the sum of the array will be 1 - 1 + 1 - 2 - 3 = -4.

Example 2

Input: nums = [1,-10,9,1], limit = 100, goal = 0

Output: 1

Constraints

  • 1 <= nums.length <= 10^5
  • 1 <= limit <= 10^6
  • -limit <= nums[i] <= limit
  • -10^9 <= goal <= 10^9

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