DFA Automaton for all words that starts with 01 and ends with 01

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$L=\left\{w \in\{0,1\}^{*} \mid \text { w starts with } 01 \text { and ends with } 01\right\}$

I need to draw a dfa and nfa , I managed to draw the nfa but the dfa didn't .. can someone lead me please?

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DFA for w that starts and ends with 01

Does the above DFA work? Start State is S, Accepting State is B, and T is a terminal state.