Modular arithmetic helps handle large numbers by working within a fixed range, often using a modulus like (10^9+7) to avoid overflow and simplify calculations.

Modular arithmetic is a foundational tool in competitive programming, particularly in problems involving large numbers. By using a modulus, such as (10^9+7) (a prime number commonly used in programming contests), we can keep numbers within a manageable range, avoiding overflow issues in languages with fixed data types. Modular arithmetic also provides efficient ways to compute with numbers in cyclic systems, making operations like addition, subtraction, and multiplication consistent and predictable. It is often used in algorithms that involve combinatorics, probability, or matrix exponentiation, where the values can grow rapidly. Familiar techniques in modular arithmetic include modular exponentiation, which allows for quick calculation of powers with a modulus, and modular inverses, which help in division within modular constraints. Mastering modular arithmetic will make you more equipped to solve problems where large numbers are involved or where calculations need to be restricted to a specific range.