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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