CF519E A and B and Lecture Rooms

Description

A and B are preparing themselves for programming contests. The University where A and B study is a set of rooms connected by corridors. Overall, the University has $ n $ rooms connected by $ n-1 $ corridors so that you can get from any room to any other one by moving along the corridors. The rooms are numbered from $ 1 $ to $ n $ . Every day А and B write contests in some rooms of their university, and after each contest they gather together in the same room and discuss problems. A and B want the distance from the rooms where problems are discussed to the rooms where contests are written to be equal. The distance between two rooms is the number of edges on the shortest path between them. As they write contests in new rooms every day, they asked you to help them find the number of possible rooms to discuss problems for each of the following $ m $ days.

Input Format

N/A

Output Format

N/A

Explanation/Hint

in the first sample there is only one room at the same distance from rooms number 2 and 3 — room number 1.