Consider a 2021-by-2021 board of unit squares. For some integer k, we say the board is tiled by k-by- k squares if it is completely covered by (possibly overlapping) k-by- k squares with their corners on the corners of the unit squares. What is the largest integer k such that the minimum number of k-by- k squares needed to tile the 2021-by-2021 board is exactly equal to 100?