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class Solution:
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    def spiralMatrixIII(
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        self, rows: int, cols: int, rStart: int, cStart: int
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    ) -> List[List[int]]:
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        ans = [[rStart, cStart]]
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        val = 1
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        i, j = rStart, cStart
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        def is_valid(i, j):
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            if 0 <= i < rows and 0 <= j < cols:
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                return True
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            return False
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        while True:
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            if len(ans) == rows * cols:
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                return ans
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            # go right val times
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            for _ in range(val):
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                j += 1
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                if is_valid(i, j):
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                    ans.append([i, j])
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            # go bottom val times
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            for _ in range(val):
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                i += 1
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                if is_valid(i, j):
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                    ans.append([i, j])
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            # go left val+1 times
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            for _ in range(val + 1):
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                j -= 1
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                if is_valid(i, j):
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                    ans.append([i, j])
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            # go up val+1 times
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            for _ in range(val + 1):
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                i -= 1
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                if is_valid(i, j):
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                    ans.append([i, j])
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            val += 2