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?
Input
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.
Constraints:
1<= T <= 100000 (10^{5})
1<= N <= 100000 (10^{5})
Note: Use fast I/O methods.
Output
For each test query, ouput the result in given format. As the result can be large answer the result modulus 1000000007 (10^{9} +7).
Case <test_query_i>: <max_section_circle_cuts_into>
Example
Input: 3
1
2
6 Output: Case 1: 1
Case 2: 2
Case 3: 31
hide comments
sanchit_aga:
20190107 13:59:37
Good question. Learnt a new formula. 

pranjulpal18:
20190103 16:15:01
Take help of https://en.m.wikipedia.org/wiki/Dividing_a_circle_into_areas


i_love_priya:
20181111 23:12:04
The answer should be the modulus of 10^9+7 .

Added by:  ad 
Date:  20181008 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  3b1b 