In competitive programming, modular arithmetic plays a crucial role in keeping numbers manageable and avoiding overflow.10⁹ + 7 (1,000,000,007) is commonly used as a mod value in competitive programming.10⁹ + 7 is the preferred choice because it is the first prime number greater than 10⁹, ensuring stability and correctness in results.10⁹ + 7 is smaller than 2,147,483,647, enabling more efficient computations using int rather than long long.