Mr President "BONUS" day!

Number Theory Level 3

Because school days are now super tiring, all the students in "Holiday Country" are protesting to the Mr. President to make the weekend longer, or else they will not go to school anymore. Mr President then make a new rule so the students will be happy :D

The new rule made week become \(8\) days and the name of the \(8\)th day is "Bonus Day", but of course Mr. President cannot change the Earth's revolution, so a year is still \(365\) days. But something happened... The biggest meteor in Galaxy, called "King Meteor" hit the sun (assume that it actually happened) and made leap years occur once in \(6\) years.

But Mr President can only apply the new rule if the year modulo \(3\) is \(2\) (Example: if the year is \(2015\), then \(2015 \equiv 2 \pmod{3}\), so Mr. President apply the rule this year.

So if today is the first day of the year \(N\) (you can call it New Year); \(N \equiv 2 \pmod{3}\); today is Bonus Day; this year is a leap year; and the first Bonus Day of the year \(N + 140\) is the \(B\)th day.

Find \(B\).


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