At the night of PKUWC2019day2, classmates (including Soetdit, TX1145967673, ZPAYAUR ,Groundhog and so on) made an amazing decision: they were ready to join together in a convoy, and they would share the night until dawn.

That night, they went online one after another. The i-th classmate will be online from .But someone reported a message: Their teacher will come at night. Everyone has a probability of  to receive the message, and one who receives the message will not go online at night. And their available time for game is when all gamers are online.So they begin to think about a question: What's expectation of the square of their available time modulo  ?

Simplified question:there are  segments , each segment has the possiblity of  to be selected, and the question is to calculate the expected value of  modulo .  means the number of  selected segment.