class Solution:
    def rotateGrid(self, grid: List[List[int]], k: int) -> List[List[int]]:
        m, n = len(grid), len(grid[0])
        nlayer = min(m // 2, n // 2) # level count
        # enumerate each layer counterclockwise starting from the top-left corner
        for layer in range(nlayer):
            r = []  # row index of each element
            c = []  # column index of each element
            val = []  # value of each element
            for i in range(layer, m - layer - 1):   # left
                r.append(i)
                c.append(layer)
                val.append(grid[i][layer])
            for j in range(layer, n - layer - 1):   # down
                r.append(m - layer - 1)
                c.append(j)
                val.append(grid[m - layer - 1][j])
            for i in range(m - layer - 1, layer, -1): # right
                r.append(i)
                c.append(n - layer - 1)
                val.append(grid[i][n - layer - 1])
            for j in range(n - layer - 1, layer, -1): # up
                r.append(layer)
                c.append(j)
                val.append(grid[layer][j])
            total = len(val)  # total number of elements in each layer
            kk = k % total    # equivalent number of rotations
            for i in range(total):
                idx = (i - kk + total) % total
                grid[r[i]][c[i]] = val[idx]
        return grid