You are given two integers n and m representing the dimensions of an $n imes m$ grid, and an integer k representing the coverage range of a sensor.

A sensor placed at a cell $(r, c)$ covers any cell $(r', c')$ in the grid that satisfies $|r - r'| \leq k$ and $|c - c'| \leq k$.

Return the minimum number of sensors required to cover every cell in the grid.

Constraints:

• $1 \leq$ n $\leq 10^3$

• $1 \leq$ m $\leq 10^3$

• $0 \leq$ k $\leq 10^3$

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