Given a m x n matrix mat and an integer k, return a matrix answer where each answer[i][j] is the sum of all elements mat[r][c] for:

• i - k <= r <= i + k,
• j - k <= c <= j + k, and
• (r, c) is a valid position in the matrix.

 

Example 1:

Input: mat = [[1,2,3],[4,5,6],[7,8,9]], k = 1
Output: [[12,21,16],[27,45,33],[24,39,28]]

Example 2:

Input: mat = [[1,2,3],[4,5,6],[7,8,9]], k = 2
Output: [[45,45,45],[45,45,45],[45,45,45]]

 

Constraints:

• m == mat.length
• n == mat[i].length
• 1 <= m, n, k <= 100
• 1 <= mat[i][j] <= 100