zero-array-transformation-ii

You are given an integer array nums of length n and a 2D array queries where queries[i] = [li, ri, vali].

Each queries[i] represents the following action on nums:

• Decrement the value at each index in the range [li, ri] in nums by at most vali.


• The amount by which each value is decremented can be chosen independently for each index.

A Zero Array is an array with all its elements equal to 0.

Return the minimum possible non-negative value of k, such that after processing the first k queries in sequence, nums becomes a Zero Array. If no such k exists, return -1.

Example 1:

Input: nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]

Output: 2

Explanation:

• For i = 0 (l = 0, r = 2, val = 1):
  
  
  
  
  • Decrement values at indices [0, 1, 2] by [1, 0, 1] respectively.
  
  
  • The array will become [1, 0, 1].
  
  
  
  


• For i = 1 (l = 0, r = 2, val = 1):
  
  
  
  • Decrement values at indices [0, 1, 2] by [1, 0, 1] respectively.
  
  
  • The array will become [0, 0, 0], which is a Zero Array. Therefore, the minimum value of k is 2.
  
  
  
  

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]

Output: -1

Explanation:

• For i = 0 (l = 1, r = 3, val = 2):
  
  
  
  
  • Decrement values at indices [1, 2, 3] by [2, 2, 1] respectively.
  
  
  • The array will become [4, 1, 0, 0].
  
  
  
  


• For i = 1 (l = 0, r = 2, val = 1):
  
  
  
  • Decrement values at indices [0, 1, 2] by [1, 1, 0] respectively.
  
  
  • The array will become [3, 0, 0, 0], which is not a Zero Array.
  
  
  
  

Constraints:

• 1 <= nums.length <= 105


• 0 <= nums[i] <= 5 * 105


• 1 <= queries.length <= 105


• queries[i].length == 3


• 0 <= li <= ri < nums.length


• 1 <= vali <= 5