How does it work with negative numbers?

The modulus operation with negative numbers can be a bit tricky. Here's how it works:

1. Definition: The result of a % b is the remainder of the division of a by b. The sign of the result is determined by the divisor (b).

2. Positive Divisor: If b is positive, the result will always be in the range [0, b). For example:

   • -10 % 3 results in 2 because -10 can be expressed as -12 + 2 (where -12 is the largest multiple of 3 less than -10).

3. Negative Divisor: If b is negative, the result will be in the range (b, 0]. For example:

   • -10 % -3 results in -1 because -10 can be expressed as -9 + (-1) (where -9 is the largest multiple of -3 less than -10).

Summary:

• The result of a % b takes the sign of b.
• The result is always adjusted to ensure it falls within the range defined by b.

This behavior can vary slightly between programming languages, so it's always good to check the specific language's documentation for details.