Combinatorics Calculator Skill Purpose Calculate combinatorial values with modular arithmetic support for competitive programming applications. Capabilities - Factorial and inverse factorial precomputation - nCr, nPr with modular arithmetic - Catalan, Stirling, Bell numbers - Lucas theorem implementation - Inclusion-exclusion principle application - Generating functions Target Processes - combinatorics-counting - number-theory-algorithms - dp-pattern-matching Combinatorial Functions Basic Counting - Factorial: n! - Permutations: P(n,r) = n!/(n-r)! - Combinations: C(n,r) = n!/(r!(n-r)!) Specia…