Mod of negative number is melting my brain

I always use my own mod function, defined as

int mod(int x, int m) {
    return (x%m + m)%m;
}

Of course, if you’re bothered about having two calls to the modulus operation, you could write it as

int mod(int x, int m) {
    int r = x%m;
    return r<0 ? r+m : r;
}

or variants thereof.

The reason it works is that “x%m” is always in the range [-m+1, m-1]. So if at all it is negative, adding m to it will put it in the positive range without changing its value modulo m.