CIRCLEDIV - Euler Puzzle
Given some set of points on a circle, you connect every pair of them with a line, find the maximum number of sections do these lines cut the circle into?
First line for each testcase file contains T denoting the no. of test queries followed by T numbers N, denoting the no. of point on a circle.
1<= T <= 100000 (105)
1<= N <= 100000 (105)
Note: Use fast I/O methods.
For each test query, ouput the result in given format. As the result can be large answer the result modulus 1000000007 (109 +7).
Case <test_query_i>: <max_section_circle_cuts_into>
6 Output: Case 1: 1
Case 2: 2
Case 3: 31
Good question. Learnt a new formula.
Take help of https://en.m.wikipedia.org/wiki/Dividing_a_circle_into_areas
The answer should be the modulus of 10^9+7 .