THINK++ — Engineering Visualized

📖 LESSON

Modular Arithmetic

In competitive programming, results are often required "modulo 10^9 + 7" to prevent integer overflow and keep the numbers within a standard range.

(a + b) % m

= ((a % m) + (b % m)) % m

(a - b) % m

= ((a % m) - (b % m) + m) % m

(a * b) % m

= ((a % m) * (b % m)) % m

(a / b) % m

= (a * b⁻¹) % m (where b⁻¹ is modular inverse)

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💡 The Negative Modulo Fix

In many languages, `-1 % 5` returns `-1` instead of `4`. To fix this, always use `(a % m + m) % m` to ensure the result is non-negative.

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