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take a look at this…

by subsequence m if you dont mean a continuous string , then it is easy ,
a naive solution i will put forward , which can be optimised .
First , check if this subsequence is present , if not 0.
If it is present , then we find the first letter of T in S , no use removing any letter before it , now two cases , we remove it or we dont remove it .
Removing it just depends if we traverse a larger string by removing it and not finding the next T , or a larger traversal by not removing it and finding the next letter of T.
Hope , you got my point though my language may not have been best .
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