Find Mr Tan's Birthday with logic!

Ben and Mark are students of Mr Tan. Mr Tan's birthday is on $N/M/1970$ and both of them know that Mr Tan's birthday is one of these $10$ dates:

$4/3/1970$

$4/6/1970$

$1/9/1970$

$1/12/1970$

$5/3/1970$

$7/6/1970$

$5/9/1970$

$2/12/1970$

$8/3/1970$

$8/12/1970$

Mr Tan tells Ben the value of $M$ and tells Marc the value of $N$ .

Then Mr Tan asks them: "Do you know when is my birthday?"

Ben says: "I don't know, but I can ensure that Mark doesn't know too."

Mark says: "Initially I don't know, but I know it now."

Ben says: "Oh! Then I know it too."

Base on the dialogue and the dates given, can you figure out which date is Mr Tan's Birthday?

Give your answer as $M+100N$

Assume Mark and Ben are amazing at their logic

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