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

You are given two strings word1 and word2. You want to construct a string merge in the following way: while either word1 or word2 are non-empty, choose one of the following options:

If word1 is non-empty, append the first character in word1 to merge and delete it from word1.

	
For example, if word1 = "abc" and merge = "dv", then after choosing this operation, word1 = "bc" and merge = "dva".


If word2 is non-empty, append the first character in word2 to merge and delete it from word2.
	
For example, if word2 = "abc" and merge = "", then after choosing this operation, word2 = "bc" and merge = "a".



Return the lexicographically largest merge you can construct.
A string a is lexicographically larger than a string b (of the same length) if in the first position where a and b differ, a has a character strictly larger than the corresponding character in b. For example, "abcd" is lexicographically larger than "abcc" because the first position they differ is at the fourth character, and d is greater than c.
 
Please complete the following python code precisely:
```python
class Solution:
    def largestMerge(self, word1: str, word2: str) -> str:
```