//     ends up at a[d], which in turn ends up at a[2d], and so on until we get back to a[0].
    //     (All indices taken mod n.) If d and n are mutually prime, all elements will have been
    //     moved at that point. Otherwise, we can rotate the cycle a[1], a[1 + d], a[1 + 2d], etc,
    //     then a[2] etc, and so on until we have rotated all elements. There are gcd(d, n) cycles