find 2 local martingales M(t) and N(t) such that M(T)=N(T),but for t<T,M(t) $\ne$ N(t)

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question:

find 2 local martingales M(t) and N(t) such that M(T)=N(T),but for t < T,M(t) $\ne $ N(t).

I can only find one is local martingale and the other one is martingale.

can you help me think of one example?