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Maximum Sum With at Most K Elements

You are given a 2D integer matrix grid of size n x m, an integer array limits of length n, and an integer k.

You are given a 2D integer matrix grid of size n x m, an integer array limits of length n, and an integer k. The task is to find the maximum sum of at most k elements from the matrix grid such that:

Return the maximum sum.

Maximum Sum With at Most K Elements diagram

Example 1

Input: grid = [[1,2],[3,4]], limits = [1,2], k = 2

Output: 7

Example 2

Input: grid = [[5,3,7],[8,2,6]], limits = [2,2], k = 3

Output: 21

Constraints

  • n == grid.length == limits.length
  • m == grid[i].length
  • 1 <= n, m <= 500
  • 0 <= grid[i][j] <= 10^5
  • 0 <= limits[i] <= m
  • 0 <= k <= min(n * m, sum(limits))

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