Please solve the programming task below using a self-contained code snippet in a markdown code block.

Given an m x n grid of characters board and a string word, return true if word exists in the grid.
The word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once.
 
Please complete the following python code precisely:
```python
class Solution:
    def exist(self, board: List[List[str]], word: str) -> bool:
```