Search in a matrix whose elements are sorted in insertion order

from typing import List
class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
        left = 0
        right = len(matrix) * len(matrix[0]) - 1

        rows = len(matrix)
        cols = len(matrix[0])

        while left <= right:
            mid = (left + right) // 2

            row_idx = mid // cols
            col_idx = mid % cols

            value = matrix[row_idx][col_idx]

            if value == target:
                return True
            elif value > target:
                right = mid - 1
            else:
                left = mid + 1

        return False