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Count Submatrices with Top-Left Element and Sum Less Than k

Medium

You receive a 0-indexed integer matrix grid and an integer k .

Produce the number of submatrices that contain the top-left element of the grid , and have a sum less than or equal to k .

Example 1

Original illustrative diagram 1 for Count Submatrices with Top-Left Element and Sum Less Than k

Input: grid = [[7,6,3],[6,6,1]], k = 18

Output: 4

Explanation: There are only 4 submatrices, shown in the image above, that contain the top-left element of grid, and have a sum less than or equal to 18.

Example 2

Original illustrative diagram 2 for Count Submatrices with Top-Left Element and Sum Less Than k

Input: grid = [[7,2,9],[1,5,0],[2,6,6]], k = 20

Output: 6

Explanation: There are only 6 submatrices, shown in the image above, that contain the top-left element of grid, and have a sum less than or equal to 20.

Constraints

  • m == grid.length
  • n == grid[i].length
  • 1 <= n, m <= 1000
  • 0 <= grid[i][j] <= 1000
  • 1 <= k <= 10^9

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