CF406E Hamming Triples

Little Chris is having a nightmare. Even in dreams all he thinks about is math. Chris dreams about $ m $ binary strings of length $ n $ , indexed with numbers from 1 to $ m $ . The most horrifying part is that the bits of each string are ordered in either ascending or descending order. For example, Chris could be dreaming about the following 4 strings of length 5: The Hamming distance $ H(a,b) $ between two strings $ a $ and $ b $ of length $ n $ is the number of positions at which the corresponding symbols are different. Сhris thinks that each three strings with different indices constitute a single triple. Chris's delusion is that he will wake up only if he counts the number of such string triples $ a $ , $ b $ , $ c $ that the sum $ H(a,b)+H(b,c)+H(c,a) $ is maximal among all the string triples constructed from the dreamed strings. Help Chris wake up from this nightmare!

The first line of input contains two space-separated integers $ n $ and $ m $ ( $ 1

Output a single integer, the number of such string triples among the given that the sum of the Hamming distances between the strings of the triple is maximal.