Mr. Cooper was a celebrated scientist who had a really big lab. There were N sticks in this lab and the length of the i-th stick was i millimeters. One day, when Mr. Cooper decided to do research on triangles, he found that M of the sticks were missed. Mr. Cooper wanted to know how many kinds of triangles could be constructed by three of the remaining sticks. Two triangles are different if and only if they are formed by different sets of sticks.
For Example, there were 8 sticks in the lab originally and the second and the sixth sticks were missed. The 7 different triangles can be constructed were (3,4,5), (3,5,7), (4,5,7), (3,7,8), (4,7,8), (5,7,8), (4,5,8).